Method for determining haemodynamic indices by use of tomographic data

ABSTRACT

Haemodynamic indices of an organ or a part of tissue are determined from a time series of tomographic data obtained by means of Magnetic Resonance Imaging. Maps of indices are produced, being significant of the dynamics of the capillary tissue flow acquired during rapid bolus injection of a tracer that stays mainly intravascular. The method may be used for evaluating the efficacy of a drug on an organ, or for obtaining information of the likelihood of recovery of an organ or part of tissue upon or during a period of insufficient vascular supply or during the progression of a chronic disease. The method may be used for discriminating between relevant therapy of an organ.

This application claims the benefit of Provisional Application No.60/126,322 filed Mar. 26, 1999

This application is the national phase under 35 U.S.C. § 371 of PCTInternational Application No. PCT/DK00/00140 which has an Internationalfiling date of Mar. 23, 2000, which designated the United States ofAmerica and was published in English.

The present invention relates to a method for determining haemodynamicindices of an organ or a part of tissue of a mammal, such as a humanbeing, from a time series of tomographic data, especially data obtainedby means of Magnetic Resonance Imaging (MRI). The method produces mapsof distribution of blood transit time as well as other indices beingsignificant of the dynamics of the capillary tissue flow fromtomographic images acquired during rapid bolus injection of a contrastagent or tracer that stays mainly intravascular in the organ. Thehaemodynamic indices may by use of the present method be obtained with aspatial resolution equal to the spatial resolution of the tomographicdata.

The method comprises the steps of conversion of tomographic images intodata representing concentrations of contrast agent as a function oftime, and the method determines the distribution of flow and meantransit time, either in absolute values or relative to the mean value,whereby the methods facilitates the (i) comparison of relative flow ortransit time distributions to that of other tissue (in particularcerebral tissue), such as normal tissue, or (ii) quantification ofabsolute flow distributions in terms of the associated extraction of asubstance with known capillary permeability.

The use of the methods for examination and monitoring of cerebralconditions of humans are of particular interest, but the method may alsobe applied to other organs, such as the heart, the liver, kidneys,tumors etc., or to other part of tissue or part of organs.

BACKGROUND

Flow and microscopic heterogeneity of flow are believed to be a maindeterminants of how efficient the delivery of nutrients andpharmaceuticals to tissue takes place. Especially in diseases wheredelivery of nutrients such as e.g. oxygen is compromised by flowreduction, determination of flow heterogeneity is therefore crucial toassess the severity of the disease. Such diseases include acute cerebralischemia, a frequent cause of death and the major cause of adultneurological disability in the Western world.

So far, the measurement of flow heterogeneity has been limited to thestudy to superficial vessels in the cortex of anaesthetised animals byhigh-speed intravital microscopy. There are no pre-existing tools thatallow determination flow heterogeneity in deeper structures, or onhumans as part of non-invasive, routine diagnostic procedures.

The study of the delivery of nutrients to the tissue is currently doneby Positron Emission Tomography (PET). Due to the costs and lack ofgeneral availability of this technique, these studies can, however, notbe performed in general patient management.

A major limiting factor in the development of new drugs in many diseasesis the cost of preclinical and clinical trials to determine beneficialeffects of new agents. In acute stroke, this is typically done bycomparing long-term neurological scores of hundreds of treated anduntreated patients. The costs of this work, as well as the total numberof patients available, therefore limits the rate at which novel drugsbecome available for common use. There exists therefore an urgent needfor techniques that in individual patients predict the progression of adisease or condition and may be used for monitoring of said progression,so that the progression for the individual patient can be assessedwhereby e.g. the efficacy of a drug or a substance can be evaluated indetails from a much more limited number of patients. Such techniques arenot currently available.

With regards to determining tissue flow, most quantitative techniquesutilise tomographic images of the distribution of radionucleidescombined with invasive blood sampling. With the spatial resolution ofsome tomographic imaging techniques, the dimensions of vessels are toosmall to accurately determine arterial tracer concentration levelsnon-invasively. Instead, image elements containing partly tissue, partlyblood vessels must be used in order to characterise the mere shape ofthe arterial input curve to the tissue. In such cases, absolute valuesof flow and volume cannot be found, and therefore a normalisationroutine allowing (i) comparison of serial measurements in a singlesubject, (ii) comparison among subjects and (iii) absolutequantification the case of susceptibility MRI of the brain is necessaryas described below.

The present invention describes and validates a new, non-invasive methodthat allows assessment of flow heterogeneity on generally availabletomographic equipment (Magnetic Resonance (MR), Computed Tomography(CT), PET). Furthermore, the technique allows indirect assessment ofmetabolic parameters.

Finally, the technique has high predictive power in terms of diseaseprogression in cerebral diseases such as ischemia, thereby providing themeans for rapid assessment of the efficacy of novel therapies.

DESCRIPTION OF THE INVENTION

It is an object of the present invention to provide a method fordetermining haemodynamic indices of an organ or part of tissue of amammal, such as a human being from tomographic data.

By haemodynamic indices is understood such indices as distribution oftransit times and parameter characterising said distribution,quantitative haemodynamic parameters obtained from said distributionsuch as parameters characterising the deviation of said distributionfrom a reference distribution, as well as other indices beingsignificant of the dynamics of the capillary tissue flow.

It is a further object of the present invention to facilitate thecomparison of relative flow distributions to a predetermineddistribution found for a normal organ (e.g. the brain) or for an organhaving a recognised disease or condition, such as having a tumour of anidentified tumour type.

It is a still further object of the invention to facilitate the abovementioned comparison for voxels of an organ.

It is a yet still further object of the present invention to providequantification of absolute flow distributions in terms of the associatedextraction of a substance with known capillary permeability.

It is an even yet still further object of the present invention toprovide the above methods so that they are applicable to human cerebraltissue.

Thus, the present invention relates to a method for determininghaemodynamic indices of an organ or part of tissue of a mammal including

a) determining a time series of tomographic data pertaining to the organor part of tissue during and after a bolus injection of a tracer dose tosaid mammal, the tracer being substantially intravascular in saidtissue,

b) determining a time series of concentration data being indicative ofthe concentration of the tracer in arteries of the organ or tissue fromthe time series of tomographic data,

c) determining a residue function of the organ or of the part of tissueby deconvolution of the time series of tomographic data with the timeseries of concentration data, and

d) determining a distribution of transit times from the slope of theresidue function.

The residue function may also be understood as a normalised impulseresponse function characterising the fraction of the tracer present inthe vascular tissue at time t after a perfect, infinitely sharp input ofa tracer in the feeding vessel. For the deconvolution a number of knownmethods may be applied, such as a Fourier transform, Box transform, butpreferably the Singular Value Decomposition is used.

The term “tomographic data” is herein understood as data representingthe concentration of the tracer, i.e. being a direct measure of theconcentration or being directly proportional to the concentration of thetracer. Thus, the “tomographic data” and the “concentration data”typically have the same physical dimension.

The distribution of transit times obtained from this method may be usedto determine a probability density function (PDF) of a normalisedhaemodynamic index, where the index is normalised by the value of theintegral of this index.

One of the haemodynamic indices obtained from the PDF may be aquantitative haemodynamic parameter, such as a parameter obtained fromcomparison of the determined PDF and a previously determined referencePDF, e.g. obtained by use of the Kolmogorov Smirnov test. The comparisonbetween the determined PDF and a reference may also includeidentification of plateau's of the curve of the PDF, distribution ofarea under the curve, area under the curve at one or the other side of acut-off value, etc.

The predetermined reference PDF used for comparison may have been foundfor a normal organ (e.g. the brain) or tissue or for an organ having arecognised disease or condition, such as having a tumour of anidentified tumour type.

Furthermore, the present invention relates to a method in which thequantitative parameter may be obtained by performing the steps of

determining the impulse response function of the organ or of the part oftissue by deconvolution of the time series of tomographic data with thetime series of concentration data,

determining the relative tissue flow from the impulse response functionof the organ or of the part of tissue,

normalising said time series of concentration data with the integral ofsaid time series of concentration data with respect to time,

determining the normalised relative tissue flow, respectively thenormalised blood volume, of the organ or part of tissue by use of therelative tissue flow and the time series of normalised concentrationdata, and

converting said normalised relative tissue flow, respectively normalisedblood volume, to an absolute value for the tissue flow, respectively theblood volume, by means of a previously determined conversion factor,

the quantitative haemodynamic parameter being of metabolic significanceand determined from the PDF and the absolute tissue flow, respectivelythe absolute blood volume.

The normalised relative tissue flow obtained from this method may beused to compare tissue flow determined from successive tomographicscanning of the same mammal in order to monitor the development of acondition of an organ or part of tissue and/or to compare tissue flow ofdifferent individuals. The comparison may be performed because the datahave been normalised which means that they are readily comparable.

The blood volume is obtained by dividing the blood flow by the meantransit time (MTT) or as the area under the tissue concentration curve(or the impulse response function) of the first pass of the bolus tracerpassage.

It is understood that the tomographic data may be obtained from avariety of methods, of which MRI and Computed Tomography (CT) arepreferred. However, for some applications it may be preferred to useother methods, such as Positron Emission Tomography (PET) or SinglePhoton Emission Computed Tomography (SPECT).

The above method may further comprise a step, wherein the normalisedrelative tissue flow, respectively the blood volume, is also normalisedwith the ratio between body weight of the individual mammal and theinjected tracer dose. By adding this step, the determined relativetissue flow is furthermore made comparable to determined relative tissueflow from tomography time series of the same individual mammal in whichthe amount of the injected tracer dose have been changed. The relativetissue flow determined for one individual mammal may furthermore becompared to relative tissue flows determined for other individuals.

The conversion factor may be a factor that is generally applicable forthe present method to members of a mammalian specie.

In particular, the conversion factor may be a factor that is generallyapplicable for the present method to an organ or tissue of the mammalianspecie.

As a special case, a parameter (E) significant for the local extractionof a substance may be determined by a method further comprising thefollowing steps:

-   -   calculating the relative flow heterogeneity (w(f)) as a function        of the relative flow (f) from the distribution of transit times,    -   estimating a value (P) for the local capillary permeability,    -   estimating a value (S) for the local capillary surface area,    -   calculating said parameter (E) as the integral value of the        relative flow heterogeneity (w(f)) multiplied by one minus the        natural exponential function of the negative ratio between

i) the product of the local capillary permeability (P) and the localcapillary surface area (S), and

ii) the product of the relative flow (f) and the absolute tissue flow(F_(t)) with respect to the relative flow (f)

The substance in question may, e.g., be oxygen, glucose or anotherimportant cellular metabolic substance or it may, e.g., be a drug oranother substance having a therapeutic effect.

Estimated values of the local capillary permeability (P) and the localcapillary surface area (S) are well-known and may be found from standardworks within the subject area.

Preferably, the normalised relative tissue flow, respectively the bloodvolume, is also normalised with the injected tracer dose being the ratiobetween tracer amount and body weight of the individual mammal.

The tomography data for the method according to the invention arepreferably obtained by means of magnetic resonance imaging, and themethod is furthermore preferably applied to cerebral tissue. Forcerebral tissue, it has been found to be advantageous to obtain thetomographic data by means of susceptibility contrast magnetic resonanceimaging.

The tissue may be renal tissue, in particular renal parenchyma tissue.

The tissue may further include tumour tissue, in particular in case thetissue is cerebral tissue.

The tracer may be a Gd-chelate, such as Gd-DTPA. It may alternatively bean ultra small iron oxide particle (USPIO) intravascular contrast agent.This is particularly preferred since an USPIO intravascular contrastagent is only transferred to the surrounding tissue to a very limitedextend. Thus, the contrast agent is mainly maintained in the blood,whereby the contrast of the resulting MR image is greatly enhanced. Thisis of particular interest in non-cerebral tissue, such as renal tissue.

The predetermined conversion factor may be a constant factor applicablefor the present method for any organ or any part of tissue of themammalian specie. Preferably, the predetermined conversion factor is aconstant factor applicable for all of cerebral tissue of the mammalianspecie, which is strongly indicated from empirical evidence.

The tomographic data discussed above and used in the present method willnormally comprise information pertaining to subregions of sections ofthe organ or part of tissue and the haemodynamic indices are determinedfor at least a substantial part of said subregions. The data of thesubregions may be represented graphically as pixel values (as agray-scale image or colour image of the section), and the quantitativehaemodynamic parameter determined from the tomograpic data may also berepresented as images subdivided into a plurality of pixels eachrepresenting a quantitative haemodynamic parameter pertaining to one ofsaid subregions.

The present invention furthermore relates to a system for processing oftime series of tomographic data pertaining to an organ or a part oftissue according to one or more of the above described methods accordingto the invention, said system residing on a computer having means forproducing an output representative of at least some of the determinedhaemodynamic indices.

The present invention further relates to a method for evaluating theefficacy of a drug or a substance on an organ or on a part of tissue ofa mammal by means of haemodynamic indices of said organ or of said partof tissue obtained by one or more of the methods according to theinvention as described above. For this use, a system residing on acomputer as described in the previous paragraph may advantageously beapplied.

The present invention further relates to a method for obtaininginformation of the likelihood of recovery of an organ or part of tissuein a living mammal upon or during a period of insufficient vascularsupply of said organ or of said part of tissue in the mammal comprisingdetermining haemodynamic indices by one or more of the methods accordingto the invention as described above.

The present invention further relates to a method for obtaininginformation of the likelihood of progression of a chronic or neoplasticdisease process of an organ or part of tissue in a living mammalaffecting said organ or said part of tissue in the mammal comprisingdetermining haemodynamic indices by one or more of the methods accordingto the invention as described above.

The present invention further relates to a method for obtaininginformation relevant for discrimination between relevant therapy of anorgan or part of tissue in a living mammal upon or a period ofinsufficient vascular supply of said organ or of said part of tissue inthe mammal comprising determining haemodynamic indices by one or more ofthe methods according to the invention as described above.

The present invention further relates to a method for obtaininginformation relevant for discriminating between relevant therapy of anorgan or part of tissue in a living mammal upon the discovery of achronic or neoplastic disease of said organ or of said part of tissue inthe mammal comprising determining haemodynamic indices by one or more ofthe methods according to the invention as described above.

Furthermore, the present invention relates to the use of informationobtained by use of one or more of the methods according to the inventionas described above for preparing a reference table for use indiscrimination of a treatment schedule for an individual mammal or groupof mammals for which information have been obtained in a manner similarto said information.

The equipment for performing the tomographic data for use in the methodaccording to the present invention is general standard equipmentavailable to such an extent that the method can be applied in routinepatient management. In addition, the determination may be performedeasily and rapidly for healthy as well severely ill patients such aspatients in coma. The method may be used for diagnosis and evaluation ofpossible further progress of disease whereby a suitable treatmentschedule may be applied.

The present method is useful in connection with detection ofheterogeneity of transit times, velocities or flows by means of externaldetection of tracers in general, whether in biological or technicalsystems. The technique is applicable to the diagnosis and study of anumber of diseases, as well as in the development and subsequentmonitoring of therapies in these diseases. Examples include:

(i) Diagnosis and treatment of diseases where, due to altered bloodsupply, tissue flow dynamics and thereby flow heterogeneity of an organis altered, e.g. myocardial infarction, acute stroke, head trauma,subarachnoidal haemorrhage, migraine, carotid stenosis, dementia.

In particular the method may be used in connection withprediction/assessment of subsequent tissue damage based on heterogeneitymeasurements in the acute phase of myocardial or cerebral infarction,evaluation of drug efficacy in these diseases based on predictions as tothe subsequent progression of the disease by heterogeneity measurements,and planning treatment based on prior knowledge of flow or transit timeheterogeneity and the associated risk of amelioration of disease.

(ii) Diagnosis, study and treatment of diseases that alter or interferewith vascular architecture in any organ or pathological tissue, suchthat normal flow or transit time heterogeneity is disturbed, e.g.: (a)Angiogenesis (the formation of new vessels) by tumors, where the randomformation of irregular vessels causes increased heterogeneity of flowsand transit times due to the passage through irregular vascular paths.(b) Vasculopathies, i.e. diseases where normal vascular wallarchitecture is disrupted, altering the passage and thereby flowheterogeneity of blood or tracer molecules, such as collagen vasculardiseases (Systemic lupus erythematosus, rheumatoid arthritis, otherconnective tissue disorders), vasculitis (giant cell arteriritis,polymylagia rheumatica), micro- and macroangiopathies in diabetes,angiopathy due to hypertension. (c) Changes in vascular architecture dueto chronic or degenerative processes of organs (liver, kidneys, heart,brain) in general.

In particular the method may be used in connection with assessment ofdisease stage (e.g. tumor grade, extent of abnormal tone in renalafferent arterioles in hypertension or acute renal failure, extent ofchange in glomerular capillary structure in degenerative renal diseases)based on heterogeneity measurements, evaluation of drug efficacy inthese diseases based on quantification of heterogeneity measurements(e.g. anti-angiogenic treatment), and planning treatment based on priorknowledge of flow or transit time heterogeneity and the associated riskof amelioration of disease.

In connection with organ transplantations it is generally of great valueto know the vascular supply and the capacity of the vascular system ofthe organ.

(iii) The study of extraction of solutes in normal or diseased tissue aspart of diagnosis or treatment. The technique can—given the capillarypermeability of a particular solute—be applied to a given organ,providing the regional extraction of the solute. Examples include thestudy of oxygen, glucose or pharmaceutical uptake in the normal ordiseased brain, e.g. acute or chronic ischemia, dementia, Parkinsonsdisease.

Accordingly, the invention relates to a method for identifying acondition relating to haemodynamic changes in an organ or tissue of amammal, diagnosis of disease, treatment or prevention of disease,monitoring of disease, and for screening of a pharmaceutically activedrug. The method involves use of the determination the tissue flow asdescribed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawingswhich are given by way of illustration only, and thus are not limitativeof the present invention and wherein:

FIG. 1 shows parametric maps of CBF for pig no. 4;

FIG. 2 shows plots of regional CBF values with their standard deviationsfor individual pigs;

FIG. 3 shows the corresponding plot for repeated PET measurement of CBFwith ¹⁵O butanol;

FIG. 4 shows CBV maps obtained with MR and PET, respectively;

FIG. 5 plots average absolute MR versus PET values of CBV forcorresponding slices under normo- and hypercapnia in 6 pigs;

FIG. 6 shows parametric CBF maps determined by PET and NMR,respectively;

FIG. 7 shows MR versus PET plots of regional CBF values along with theirstandard deviations for the six volunteers;

FIG. 8 shows the conventional MRI as well as the PET CBF maps from thevolunteer 6 and what may reflect a methodological problem of the MRtechnique;

FIG. 9 shows how flow estimates become increasingly underestimated asthe arrival delay of the tracer at a brain region increases, in both PETand MR CBF measurements;

FIG. 10 shows that the vasculature was modeled a major, feeding arteryin series with 20 small vessels in parallel;

FIG. 11 shows a set of typical tissue and arterial concentration timecurves obtained from volunteer 1;

FIG. 12 shows the location and size of three regions chosen fordetermination of flow heterogeneity in volunteer 4;

FIG. 13 a shows all pairs of relative transit time t and correspondingh(t) measured for all regions in all 6 volunteers;

FIG. 13 b shows under the assumption of equal capillary lengths thecorresponding plot of relative flow f and w(f) measured for all regionsand volunteers;

FIG. 14 shows a typical set of tissue concentration time curves as wellas the fits provided by the model;

FIG. 15 shows gray:white matter flow ratios determined by the modelapproach plotted versus corresponding ratios in identical regionsdetermined by the SVD approach;

FIG. 16 a shows the effect of AIF delay on fitted flow rates for thevascular model and the SVD approach, respectively;

FIG. 16 b shows the fitted feeding artery volume as a function of delay;

FIG. 17 shows the means and standard deviation of the fitted flow ratesfor two sets of simulated data (V_(art)−0.5, F_(p)=60 m/100 ml/min,V_(p)=3%; V_(art)=0.5%, F_(p)=20 ml/100 ml/min, V_(P)=2%), using themodel (FIG. 17 a) and SVD (FIG. 17 b) approach, respectively;

FIG. 18 shows fitted flow rates versus corresponding fitted feedingartery volumes from simulated curves with SNR-40;

FIG. 19 shows the findings of Hudetz et al. and Abounader et al. alongwith the relative plasma flows;

FIGS. 20 a, 20 b, and 20 c show a typical pattern of patient 6;

FIGS. 21 a and 21 b show the initial DWI, initial MIT, initial p/CBF andfollow-up FLAIR images of patient 11.

FIG. 22 shows that final infarct volumes are compared to the initialabnormalities of DWI+MTT and DWI+p maps, repectively;

FIGS. 23 a and 23 b show the respective maps from patient 3;

FIGS. 24 a and 24 b show maps from patient 9;

FIG. 25 shown one slice from this patient, displaying areas with p<0.1;

FIG. 26 shows the qualitative analysis of the kinetics of oxygendelivery.

FIG. 27 shows typical parametric renal flow images acquired immediatelyafter and 105 minutes after ureteral occlusion;

FIG. 28 shows the temporal evolution of renal plasma flow and volumeafter ureteral occlusion;

FIG. 29 shows transit time characteristics measured as the averagedtransport functions in 4 pixels from to regions; and

FIG. 30 shows structural T₂-weighted image (left) of a female with agrade II astrocytoma, showing edema in the medial part of the leftparietal lobe.

DETAILED DESCRIPTION OF PREFERRED METHODS ACCORDING TO THE INVENTION

The present method produces maps of normalised relative or absolutetissue blood flow, blood volume and absolute blood mean transit timefrom dynamic, tomographic images acquired during rapid bolus injectionof a contrast agent or tracer that stays mainly intravascular in theorgan.

By ‘blood volume’ is understood tracer or contrast agent distributionvolume per tissue volume. If the distribution volume is less than thatof total blood (e.g. only plasma), it is understood that conversion toabsolute blood volume can be achieved by knowledge of regionaldistribution volume characteristics, e.g. haematocrit, or othernormalisation by an independent techniques (e.g. positron emissiontomography) as presented in this description. Likewise, ‘blood flow’refers to flow of tracer or contrast agent distribution volume pertissue volume per unit time, with the aforementioned method ofconversion to blood flow. Finally, ‘transit time’ refers to the timetaken for tracer or contrast agent to traverse the image element, thearrival at which is defined from the arterial input measurement.

Furthermore, the method determines the distribution of flow and meantransit time, either in absolute values or relative to the mean value.The methods further allows the (i) comparison of relative flowdistributions to that of normal tissue (here brain) or (ii)quantification of absolute flow distributions in terms of the associatedextraction of a substance with known capillary permeability.

With the resolution of some tomographic imaging techniques, thedimensions of vessels are too small to accurately determine arterialtracer concentration levels non-invasively.

Instead, image elements containing partly tissue, partly blood vessels,must be used in order to characterise the mere shape of the arterialinput curve to the tissue. In such cases, absolute values of flow andvolume cannot be found, and therefore a normalisation routine allowing(a) comparison of serial measurements in a single subject, (b)comparison among subjects and (c) absolute quantification the case ofsusceptibility MRI of the brain is described below.

Overview

The techniques consist of the following steps:

-   A. Conversion of tomographic images into images representing    concentrations of contrast agent as a function of time.-   B. Identification of relative or absolute (i.e. in units identical    to those of the tomographic images after the above mentioned    conversion) arterial tracer concentrations from the image data.-   C. In the case of relative arterial tracer concentrations,    -   normalisation of the arterial input area to the injected dose of        contrast agent per kg body weight.-   D. Optional correction of tissue tracer curves for delays.-   E. Determination of    -   (i) absolute or relative tissue blood flow    -   (ii) tissue impulse response function    -    by deconvolution of tissue concentration time curves by the        arterial tracer concentration in each image element.-   F. Determination of tissue blood volume by determining the area    under the tissue first-pass concentration curve.-   G. Determination of tissue mean transit time by the tissue blood    volume—blood flow ratio.-   H. In the case of MR susceptibility contrast imaging using    Gd-chelates in brain tissue, conversion to absolute blood flow and    blood volume by a pre-determined constant.-   I. Determination of the distribution of flow or transit times in    each image element from the residue function (normalised impulse    response function) determined in E.-   J. Comparison of distributions of relative flows to a predetermined    distribution found for a normal organ, here brain.-   K Quantification of the distribution of flows in terms of the    extraction fraction of a given solute with specified capillary    permeability, in cases where imaging is performed with MR imaging    with microvascular weighting, or microvascular volume can otherwise    be inferred from total blood volumes.    1. Conversion of Tomographic Data into Tracer Concentration Images

The method and associated software handles various modalities, dependingon whether tracer injection changes signal intensity from baseline in alinear or logarithmic fashion upon tracer arrival. With a specifiedoption, acquired tomographic images during tracer bolus injection areconverted into concentrations as a function of time, with measurementtime points spaced equally in time.

1.1. In the case of MR images, weighted towards the transverserelaxation times (T₂ or T₂′), (typically acquired in brain), the tissueconcentration as a function of time, C₁(t), is typically obtained by theformula

$\begin{matrix}{{C_{t}(t)} = {{- k} \cdot {{\log\left( \frac{S(t)}{S\left( t_{o} \right)} \right)}/{TE}}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$where S(t₀) is the signal intensity before contrast injection (formed asthe average of signal intensities up to tracer arrival), S(t) is thesignal intensity at time t, and TE is the echo time used in thesequence. Here, k is a constant characteristic of the tissue andcontrast agent.

1.2. In the case of MR images weighted towards the longitudinalrelaxation time (T₁) images (typically acquired for intravasculartracers in the heart), concentrations are assessed directly by thechange in longitudinal relaxation rate, ΔR₁, as derived from signalintensity changesC _(t)(t)=

·ΔR ₁  Eq. 2where

is the relaxivity of the applied contrast agent.

1.3. In the case of Computed Tomography (CT) images, concentrations areassessed by the change in image intensity, measured in Hounsfield units,ΔHC _(t)(t)=κ·ΔH  Eq. 3where κ is the characteristic X-ray absorption of the contrast agent.2. Identification of Arterial Vessels

For identification of arterial vessels in the image, the algorithmprovides the choice of first producing an image that guides this process(2.a.), or proceeding directly to calculation of tissue flow (2.b.)

2.a. If so specified by an option, the concentration time curve of eachimage element is fitted to a gamma variate function by nonlinearleast-squared regression (by means of a fletcher-algorithm) over thetime interval until visible tracer re-circulation occurs (there-circulation is specified by the user, determining

-   -   (a) Tracer arrival time    -   (b) Area under first pass (this quantity is proportional to the        local blood volume).

These two quantities are stored as floating point binary image file,allowing visualisation as an image where each image pixel corresponds toquantities (a) and (b), respectively. An artery is then visuallyidentified in these images by

-   -   (a) Anatomical location.    -   (b) Early tracer arrival relative to the arrival in tissue.    -   (c) Large area under first pass (corresponding to a large blood        volume and thereby a large portion of the vascular volume being        contained in a voxel).

2.b. By observing images of tracer concentration as a function of timein a tool that allows visualisation of the time-course of single pixels,arterial levels can be identified.

Upon identification of the arterial input function, the correspondingsignal intensity time curve is fed to the program below in the form ofan ASCII file.

3. Normalisation of Arterial Input to Allow Comparison of SerialMeasurements

In cases where arterial concentrations are not known in the units oftissue concentrations the algorithm includes a method to allowcomparison of relative tissue blood flow and tissue blood volume inserial examinations in the same subject or animal. In order to achievethis, the area of the arterial input function (as determined by gammavariate fitting above) is set equal to the injected dose (in millimoles)normalised per body weight prior to the deconvolution below. Likewise,subsequent blood volume measurements are divided by the aforementioned,dose-corrected arterial input area.

4. Determination of Blood Volume

Using known tracer kinetic principles, relative blood volume isdetermined as the area under the tissue concentration time curvecorresponding to the first-pass of the injected tracer or contrast agent(See e.g. FIG. 2 in Example 1), normalised to the arterial input areadetermined in 3. The area is determined both by direct, numericalintegration, and by gamma variate fitting (See section 2).

5. Determination of Blood Flow and Mean Transit Time

Tissue flow, F_(t), is determined as the solution to the equationC _(t)(t)=F _(t) ·C _(a)(t){circle around (×)}R(t)  Eq. 4where {circle around (×)} denotes convolution, C_(a)(t) is the arterialconcentration as a function of time, and R(t) is the residue function,describing the fraction of particles still present in the vasculature attime t after a unit impulse input.

Mean Transit time (MTT) is given from the blood volume (V) and F_(t) thecentral volume theorem

$\begin{matrix}{{MTT} = \frac{V}{F_{t}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

With tissue and arterial concentrations measured at equidistant timepoints t₁, t₂=t₁+Δt, . . . , t_(N), Equation 4 can be reformulated as amatrix equation

$\begin{matrix}{\begin{pmatrix}{C_{t}\left( t_{1} \right)} \\{C_{t}\left( t_{2} \right)} \\\ldots \\{C_{t}\left( t_{N} \right)}\end{pmatrix} = {{F_{t} \cdot \Delta}\;{{t\begin{pmatrix}{C_{a}\left( t_{1} \right)} & 0 & \ldots & 0 \\{C_{a}\left( t_{2} \right)} & {C_{a}\left( t_{1} \right)} & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots \\{C_{a}\left( t_{N} \right)} & {C_{a}\left( t_{N - 1} \right)} & \ldots & {C_{a}\left( t_{1} \right)}\end{pmatrix}} \cdot \begin{pmatrix}{R\left( t_{1} \right)} \\{R\left( t_{2} \right)} \\\ldots \\{R\left( t_{N} \right)}\end{pmatrix}}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

The equation is (after applying Simpsons rule to the matrix elements(Østergaard 1996b)) solved for F_(t)·R(t) in each pixel by SingularValue Decomposition (SVD), with a cut-off in diagonal eigenvalues at 20%of the maximum value in order to suppress experimental noise typical oftomographic images (signal to noise ratio of the order of 10). The noisecut-off of 20% is user specified. In the case of higher signal-to-noiseratio (SNR) or specific SNR characteristics, a Monte Carlo simulationscheme is provided to optimise the cut-off (Østergaard 1996b).

The algorithm allows independent correction for tracer arrival delaysprior to deconvolution by shifting the tissue curve in a given pixel bythe delay fitted in 2.a., thereby reducing bias in flow rates due tosimple delays of the tissue curve relative to the arterial input curve(Østergaard 1996a).

The algorithm calculates the following quantities, and stores them asdigital, floating point images:

-   -   (a) Tissue blood volume (As determined section 2.a. and 4).    -   (b) Tissue blood volume (As determined by simple, numerical        integration up to tracer re-circulation—section 4).    -   (c) Blood mean transit time determined as the area under the        residue function response R(t).    -   (d) Relative or absolute tissue flow as determined by the        maximum value of the impulse response function (Ft-R(t))—Section        5.        -   Here, relative flow, F_(r), means a value proportional to            (by the same factor throughout the digitised images of            relative flows) absolute flow in cases where absolute            arterial flow values cannot be determined. Again, absolute            flow refers to cases where arterial concentrations are known            in the units of the tissue concentration data.    -   (e) Relative or absolute tissue flow as determined by Equation        5, using the blood volume determined in (b) divided by the MTT        determined in (c).        -   Here, relative flow means a value proportional to (by the            same factor throughout the digitised images of relative            flows) absolute flow in cases where absolute arterial flow            values cannot be determined. As above, an absolute flow            refers to the cases where arterial concentrations are known            in the units of the tissue data.    -   (f) MTT determined as tissue blood volume (b) divided by tissue        flow (d) (Equation 5)    -   (g) The tissue residue function, R(t).    -   (h) The goodness of fit, χ², of Equation 4 to the tissue        concentration time curve.        6. Absolute Quantification

To allow absolute quantification of cerebral blood flow (CBF; ml/100ml/min) or cerebral blood volume (CBV, ml/100 ml) measurements withGd-chelates and dynamic T₂ weighted susceptibility contrast agentsvalues are determined as

-   -   CBF=0.87·B_(o)·F_(r) (humans)    -   CBV=0.87·B_(o)·V_(r) (humans)    -   CBF=1.09·B_(o)·F_(r) (porcine data)    -   CBV=1.09·B_(o)·V_(r) (porcine data)

Where B_(o) is the field strength of the magnet in Tesla, and V_(r) andF_(r) are the relative volumes and flows determined as described insection 4 and 5, respectively, where impulse response height and tissuecurve area have been appropriately corrected for the arterial inputarea.

7. Determining the Distribution of Transit Times

To determine the distribution of tissue transit times, h(t), thenegative slope of the tissue residue function is determined in eachpoint as the average of slopes of straight lines connecting the previousand following point on the R(t) curve (See Equation 21 and Equation 22).

Special Cases:

-   -   7.a. At the initial point of R(t), where only one slope can be        defined, the slope of the straight line connecting the initial        and second measurement of R(t) is chosen    -   7.b. In cases where, due to noise, R(t) between to points        deviates from being either constant or decreasing as a function        of time, the slope is set to zero.

The resulting curve, with the time axis normalised to the mean transittime, is illustrated in Example 2 (Østergaard 1998a).

8. Determining the Distribution of Relative Flows.

In the remainder of the description, relative flows refer to a definedfraction of the mean flow, i.e. a dimensionless quantity, independent ofany absolute quantification of flow.

Under the assumption of equal lengths of capillary paths, thedistribution of transit times can be converted into a distribution w(f)of relative flows f (i.e. flows normalised such that the mean of thedistribution is 1) by the relation

$\begin{matrix}{{f \cdot F_{t}} = \frac{V}{t}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$where V is the associated blood volume (Units of V and F_(t) may here bearbitrary due to the normalisation in Equation 9), and thereby

$\begin{matrix}{{w(f)} = {{- \frac{t}{f}} \cdot {h(t)}}} & {{Eq}.\mspace{14mu} 8}\end{matrix}$where t is a given transit time in the distribution above, h(t) thecorresponding negative slope of R(t) and dt is given by the timeresolution of the measurements (and thereby R(t)).

Its is finally required that the resulting curve w(f) be a probabilitydensity function (PDF), i.e. has area 1, and has mean value 1 (i.e.describes flows relative to total flow), i.e.

$\begin{matrix}{{\int_{0}^{\infty}{{w(f)}f{\mathbb{d}f}}} = {{\int_{0}^{\infty}{{w(f)}{\mathbb{d}f}}} = 1}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$

This is achieved by iteration, numerically integrating the expressionsof w(f) and f above, in each step dividing f and w(f) by the precedingintegral.

9. Determining Abnormal Flow Distributions

The resulting distribution of relative flows is recalculated by linearinterpolation to determine its values at predefined relative flow valuespreviously determined for normal tissue (FIG. 13 b in Example 3).

The values read

TABLE 1 f w(f) f w(f) 3.8053 1.65E-03 0.6941 1.4594 2.865 0.0226 0.6471.5915 2.3306 0.0372 0.6205 1.6279 1.7879 0.0627 0.5969 1.5812 1.58810.1198 0.5815 1.351 1.4459 0.1751 0.565 1.3393 1.3535 0.2491 0.54481.2367 1.2785 0.3303 0.5262 1.1433 1.1912 0.4058 0.5133 1.0688 1.11060.4793 0.5007 0.928 1.0474 0.646 0.4822 0.6559 0.9972 0.7218 0.46890.6366 0.9438 0.9032 0.4571 0.4282 0.8981 0.986 0.4416 0.3133 0.82141.1098 0.4316 0.0244 0.7794 1.3562 0.42 0

In each image element, the distribution is compared to this standardcurve by means of a nonparametric Kolmogorov Smirnov (KS) test, and thecorresponding p value is calculated.

The program returns digitized images of

-   -   8.a. The KS probability p as a quantitative measure of deviation        from the normal distribution.    -   8.b. 20 images containing the values of w(f) at the predefined        values f in Table 1.    -   8.c. With a specified option, corresponding comparison of the        distribution of relative transit times is performed (with the        curve in FIG. 13 a in Example 3), and the transit times or        relative transit times displayed.        10. Absolute Quantification of Flow heterogeneity and Solute        Extraction

With a specified option, for susceptibility contrast MR imaging, theprogram combines the relative flow heterogeneity w(f) with absolute flowestimates (See Section 5) to calculates distribution of absolute flowsin ml/1100 ml/min. Furthermore, using the microvascular weighting (Forexample as demonstrated in Example 1 or in Østergaard 1998c) and tablevalues for the microvascular dimensions of the organ in question (forbrain capillaries e.g. 8 μm diameter and 120 μm length), blood volume isconverted into capillary surface area, S. The local extraction E of asubstance with capillary permeability P (as given by literature values),is then given by:

$\begin{matrix}{E = {\int_{0}^{\infty}{{w(f)}\left( {1 - e^{- \frac{PS}{f\mspace{11mu} F_{t}}}} \right){\mathbb{d}f}}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

This quantity is visualised as a separate image, based on the specifiedvalue of P. In cases where tomographic images do not possess a specificmicrovascular weighting, S can be inferred from the blood volume byliterature values describing microvascular dimensions and fractions forthe relevant organ.

EXAMPLE 1

Absolute Cerebral Blood Flow and Blood Volume Measured by MRI BolusTracking: Comparison with Pet Values

Summary of the Example

Cerebral blood flow (CBF) was determined with magnetic resonance imaging(MRI) of contrast agent bolus passage, and compared the results to thoseobtained by positron emission tomography (PET). Six pigs were examinedby MRI and PET under normo- and hypercapnic conditions. After dosenormalisation and introduction of an empirical constant Φ_(Gd), absoluteregional CBF was calculated from MRI. The spatial resolution and thesignal-to-noise-ratio of CBF measurements by MRI were better than by theH₂ ¹⁵O-PET protocol.

MRI Cerebral Blood Volume (CBV) estimates obtained using thisnormalisation constant correlated well with C¹⁵O-PET CBV values However,PET CBV values were about 2.5 times larger than absolute MRI CBV values,supporting the hypothesised sensitivity of MRI to small vessels.

Background

Rapid magnetic resonance imaging of the passage of a bolus of magneticsusceptibility contrast agent has become an important tool for assessingregional cerebral blood volume (CBV, ‘perfusion’) (Rosen et al., 1990;Rosen et al., 1991). This technique has gained widespread acceptance inthe evaluation of certain types of haemodynamic changes in cerebralpathologies, especially stroke (Sorensen et al., 1996) and CNS tumors(Aronen et al. 1994).

With regard to cerebral blood flow (CBF) determined from contrast boluspassage, there has been uncertainty whether CBF can be measured reliablywith MRI, due to inherent theoretical problems (Lassen, 1984; Weisskoff,1993). Recent results indicate that MRI can be used to measure CBF, inthat mean gray:white matter flow ratios measured by dynamic spin echo(SE) echo planar imaging (EPI) in normal humans were similar to PETliterature ratios for CBF for age-matched subjects (Østergaard et al.1996a; Østergaard et al 1996b). The bolus technique has only been ableto yield relative CBF values within a given subject. In this report, wepresent a procedure for determining absolute CBF values by means of MRI.We compared the CBF values to the results of the PET [¹⁵O] waterclearance method in hypercapnic animals. We also studied themicrovascular sensitivity of MRI CBV measurements, comparingquantitative CBV measured with MRI by our approach, and PET [¹⁵O]COestimates of vascular volume.

Theory

MRI CBF Measurements

A detailed discussion of the method of measurement of CBF by MR imagingof nondiffusible tracers is presented elsewhere (Østergaard et al.,1996b). In brief, the concentration C_(VOI)(t) of an intravascularcontrast agent within a given volume of interest (VOI) can be expressedas

$\begin{matrix}{{C_{VOI}(t)} = {F \cdot {\int_{0}^{t}{{C_{a}(\tau)}{R\left( {t - \tau} \right)}{\mathbb{d}\tau}}}}} & {{Eq}.\mspace{14mu} 11}\end{matrix}$where C_(a)(t) is the arterial input, F is tissue blood flow and R(t) isthe vascular residue function, i.e. the fraction of tracer present inthe vascular bed of the VOI at time t after injection of a unit impulseof tracer in its supply vessel. By treating the residue function as anunknown variable, this approach circumvents the problems of usingintravascular tracers for CBF measurements pointed out by Lassen (1984)and Weiskoff et al. (1994). Assuming that tissue and arterialconcentrations are measured at equidistant time points t₁, t₂=t₁+Δt, . .. , t_(N), this equation can be reformulated as a matrix equation

$\begin{matrix}{\begin{pmatrix}{C_{VOI}\left( t_{1} \right)} \\{C_{VOI}\left( t_{2} \right)} \\\ldots \\{C_{VOI}\left( t_{N} \right)}\end{pmatrix} = {{{CBF} \cdot \Delta}\;{{t\begin{pmatrix}{C_{a}\left( t_{1} \right)} & 0 & \ldots & 0 \\{C_{a}\left( t_{2} \right)} & {C_{a}\left( t_{1} \right)} & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots \\{C_{a}\left( t_{N} \right)} & {C_{a}\left( t_{N - 1} \right)} & \ldots & {C_{a}\left( t_{1} \right)}\end{pmatrix}} \cdot \begin{pmatrix}{R\left( t_{1} \right)} \\{R\left( t_{2} \right)} \\\ldots \\{R\left( t_{N} \right)}\end{pmatrix}}}} & {{Eq}.\mspace{14mu} 12}\end{matrix}$and solved for CBF·R(t) by algorithms from linear algebra. Østergaard etal. (1996a) demonstrated that, by using singular value decomposition(SVD), R(t) and CBF can be determined with good accuracy, independent ofthe underlying vascular structure and volume, and with raw image signalto noise ratios (SNR) equivalent to those obtainable in current clinicalMR imaging protocols.MRI CBV Measurement

Vascular volume was determined by numerically integrating the area underthe concentration time curve during the contrast bolus

$\begin{matrix}{{CBV} \propto {\int_{bolus}{{C_{VOI}(\tau)}{\mathbb{d}\tau}}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$(Stewart, 1894). Absolute tracer concentrations are not readilyavailable by means of the susceptibility contrast measurements used inthis study (See below). However, as CBF and CBV are obtained from thesame, arbitrary concentration units, the empirical constant that yieldstrue, absolute CBF found below will also provide absolute CBV values.PET CBF Measurement.

The regional uptake of a diffusible tracer is described by the equationintroduced by Ohta et al. (1996):

$\begin{matrix}{{C_{VOI}(t)} = {{\left( {1 - V_{0}} \right) \cdot K_{1} \cdot {\int_{0}^{t}{{C_{a}(\tau)}e^{- {k_{2}{({t - \tau})}}}{\mathbb{d}\tau}}}} + {V_{0} \cdot {C_{a}(t)}}}} & {{Eq}.\mspace{14mu} 14}\end{matrix}$where, by assumption, K₁=CBF for freely diffusible tracers and

${k_{2} = \frac{K_{1}}{Ve}},$where V_(e) is the partition volume of the tracer. V₀ is the vasculardistribution volume for the tracer in the tissue.Material and MethodsAnimal Preparation and Experimental Protocol

Six female country-bred Yorkshire pigs weighing 38–45 kg were used inthe experiments. Prior to the experiment, the pigs were housed singly installs in a thermostatically controlled (20° C.) animal colony withnatural lighting conditions. The pigs had free access to water but weredeprived of food for 24 hours prior to experiments. The project wasapproved by the Danish National Committee for Ethics in Animal Research.Pigs were initially sedated by i.m. injection of 0.25 ml/kg of a mixtureof midazolam (2.5 mg/ml) and ketamine HCl (25 mg/ml). A catheter wasthen placed in an ear vein. After i.v. injection of additionalmidazolam/ketamine mixture (0.25 ml/kg), the pig was intubated andartificially ventilated (Engström, Sweden) throughout the experiment,maintaining anaesthesia by continuous infusion of 0.5 ml/kg/hr of themidazolam/ketamine mixture and 0.1 mg/kg/hr pancuronium. Indwellingfemoral arterial and venous catheters (Avanti® size 4F–7F) weresurgically installed. Infusions of isotonic saline (approx. 100 ml/hr)and 5% glucose (approx. 20 ml/hr) were administered i.v. throughout theexperiments. Throughout the PET-experiment, body temperature, bloodpressure, heart rate and expired air CO₂ levels were monitoredcontinuously (Kivex, Ballerup, Denmark), and arterial blood sampleswithdrawn and analysed (ABL 300, Radiometer, Copenhagen) at regularintervals to monitor blood gases and whole blood acid-base parameters.In the MR-scanner, expired air CO₂ was monitored continuously (DatexCapintec 2000). Hypercapnia was induced by decreasing respiratory rateand tidal volume. The animal was allowed one hour to equilibrate to asteady P_(a)CO₂ level. At the end of experiments, the anaesthetised pigswere killed in accordance with the regulations of the Danish NationalEthics Committee for Animal Experiments.

MRI Imaging Protocol

Imaging was performed using a GE Signa Horizon 1.0 Tesla imager (GEMedical Systems, Europe). Following a sagittal scout, a T₁-weighted 3Dgradient echo sequence (time of repetition−TR=8 ms, time of echo−TE=1.5ms, 20° flip angle) was acquired for later co-registration of MR and PETdata. For dynamic imaging of bolus passages, spin echo (TR=1000 ms TE=75ms) single shot echo planar imaging (EPI) was performed, starting 30seconds prior to injection. A 64×64 acquisition matrix was used with a14×14 cm coronal field of view (FOV), leading to an in-plane resolutionof 2.2×2.2 mm². The slice thickness was 6 mm.

In all experiments, bolus injection of 0.2 mmol/kg Gadodiamide(OMNISCAN®, Nycomed Imaging, Oslo, Norway) was performed manually at arate of 15–20 mils. Prior to the first dose, a pre-dose of 0.05 mmol/kgwas given to avoid systematic effects from changes in blood T₁.

MRI Image Analysis

We used susceptibility contrast arising from compartmentalisation of theparamagnetic contrast agent (Villringer et al., 1988) to determinetissue and arterial tracer levels. We assumed a linear relationship(Weisskoff et al., 1994) between paramagnetic contrast agentconcentration and the change in transverse relaxation rate ΔR₂, so as todetermine tissue and arterial tracer time concentration curves C(t)according to the equation

$\begin{matrix}{{{C(t)} \propto {\Delta\;{R_{2}(t)}}} = {{- {\log\left( \frac{S(t)}{S(0)} \right)}}/{TE}}} & {{Eq}.\mspace{14mu} 15}\end{matrix}$where S(O) and S(t) are the signal intensities at the baseline and timet, respectively. Notice that we assumed T₁ to be unaltered during thebolus injection. Notice that this equation does not provide absoluteconcentrations. In our approach, we fixed the relation betweensusceptibility contrast and tracer concentration by requiring MR flowrates in susceptibility contrast units to equal absolute flow ratesmeasured by PET. The resulting constant of proportionality, Φ_(Gd), isthe used to calibrate MR measurements of both CBF and CBV to absolutevalues.

The arterial concentration was determined in each animal from pixelscontaining large, feeding vessels (typically the middle cerebral artery)showing an early and large (3–10 times that of gray and white matter)increase in ΔR₂ following contrast injection. This method has previouslybeen demonstrated to closely reflect actual, arterial levels for thesusceptibility contrast agents used in this study when imaged using spinecho EPI techniques (Porkka et al., 1991). The integrated area of thearterial input curve was in each measurement normalised to the injectedcontrast dose (in mM per kg body weight) in order to compare within andamong animals.

To determine CBF from equation 12, the deconvolution was performed overthe range of measurements where the arterial input values exceeded thenoise level (usually about 15 seconds). Deconvolution followed smoothingof raw image data by a 3×3 uniform smoothing kernel to. The maximum ofthe deconvolved response curve was assumed proportional to CBF. CBV wasdetermined by numerically integrating the concentration time curve frombolus arrival to tracer re-circulation.

PET Radiochemistry

¹⁵O₂ was produced by the ¹⁴N(d,n)¹⁵O nuclear reaction by the bombardmentof nitrogen gas with 8.4 MeV deuterons using a GE PETtrace 200cyclotron. ¹⁵O₂ was mixed with hydrogen and passed in a stream ofnitrogen gas over a palladium catalyst at 150° C. to produce ¹⁵O-watervapour, which was trapped in 10 ml sterile saline. ¹⁵O—CO was preparedby passing ¹⁵O₂ in a stream of nitrogen gas over activated carbon at900° C. The ¹⁵O—CO was piped directly to a 500 ml vial in a dosecalibrator situated close to the PET scanner. Upon decay to the requiredradioactivity, the ¹⁵O—CO was administered to the pig as describedbelow. ¹⁵O-Butanol was prepared by the reduction of ¹⁵O₂ withtri-n-butyl borane immobilised on an aluminum solid phase matrix. Theproduct was purified by transfer of the resulting radioactivity with 10ml H₂O onto a C18 solid phase extraction column. The ¹⁵O-butanol wassubsequently eluted into a sterile vial with 10 ml 20% ethanol.

PET Imaging Protocol

The pigs were studied lying supine in the scanner (Siemens ECAT EXACTHR) with the head in a custom-made head-holder. The position of the headwas checked throughout the experiment with laser markers. To measureCBF, i.v. injection 800 MBq H₂ ¹⁵O was performed, followed immediatelyby an i.v. injection of 3–4 ml of heparin solution (20 IU/1 I isotonicsaline) to flush the catheter. We acquired a sequence of 21 (One sampleevery fifth second for 60 s, one sample every tenth second for oneminute and one sample every 20^(th) second for 1 minute) arterial bloodsamples (1–2 ml) and 12 PET brain images (One image every tenth secondfor one minute, one image every 15^(th) s for one minute and one imageevery 30^(th) s for the remaining 60 s). To measure CBV, we administered800 MBq ¹⁵O labeled CO mixed with oxygen to a 1 l volume by syringe.Following ten seconds breath-hold, normal ventilation resumed. To assessthe variability of repeated CBF results, an additional injection of¹⁵O-butanol was performed in one pig, using the imaging and bloodsampling scheme described above. For all experiments, totalradioactivity in blood samples was measured, and image as well asarterial data were corrected for the half-life of ¹⁵O (123 s). PET imagedata were reconstructed using a Hann filter with a cutoff frequency of0.5 pixel⁻¹, resulting in a spatial resolution (FWHM) of 4.6 mm.Correction for attenuation was made on the basis of the transmissionscan.

PET Image Analysis

High SNR PET data were used to co-register PET and MR data usingREGISTER (courtesy David McDonald and Peter Neelin, MontrealNeurological Institute, McGill University, Montreal, Canada). Raw PETimage data were then transformed and re-sampled to the same spatiallocation and resolution as the MR data to allow direct comparison of thetwo techniques. Following the application of the 3×3 uniform smoothingkernel to the raw PET images, the ¹⁵O water data was fitted to equation14 using non-linear, least squared regression analysis of each imagevoxel. CBV was determined by the ratio of cerebral and arterial wholeblood ¹⁵O CO levels after initial distribution (30 seconds) of thetracer. We assumed that the mean brain-to-systemic haematocrit ratio is0.68 (Lammertsma et al., 1984). To correct for slightly differentP_(a)CO₂ levels in the MRI and PET normo- and hypercapnic conditions,respectively, the PET CBF and CBV maps were corrected to the P_(a)CO₂ ofthe MRI measurements. We assumed a linear relationship between P_(a)CO₂,and CBV and CBF, respectively (Grubb et al., 1974), i.e.CBF=a·P _(a)CO₂ +b

The two constants a and b were determined for each pixel, and CBV andCBF were corrected.

Comparison of PET and MR Parameter Images

MRI CBF maps were filtered using a 4.5 mm FWHM gaussian filter to makethe spatial resolution of PET and MR maps approximately identical. Pixelmaps of CBF (at similar anatomical locations and pixel size) generatedwith PET and MRI were then compared on a regional basis for the normo-and hypercapnic condition. In each image, 10–12 regions of interest(ROI) of similar size were chosen. Average regional CBF values and theirstandard deviations (derived from the pixels within the ROI) for thenormo- and hypercapnic conditions were then plotted versus thecorresponding PET CBF values to examine the appropriateness of a linearrelationship between the two estimates. Linear least squared regressionanalysis was performed to determine the slope and y intercept of thelinear fit Finally, to test whether a common conversion factor yieldsabsolute CBF by MRI, 2-way ANOVA was performed, comparing the slope andits standard deviation for each pig to the remaining pigs.

Results

By averaging regional MRI CBF values (As determined by equation 12 and15) and ¹⁵O water PET CBF values (in ml/100 ml/min) for all pigs (forboth normo- and hypercapnic conditions), a conversion factor ofΦ_(Gd)=1.09 was found. In the remaining analysis, all MR flow rates weremultiplied by this factor.

FIG. 1 shows parametric maps of CBF for pig no. 4. The pixel size is thesame in the two images. Notice the good overall agreement between theregional values and responses to arterial CO₂ levels using the twomethods, although the MRI CBF map appears to distinguish better betweengray and white matter structures than the PET CBF maps. Notice also thatthe PET CBF map appears to be somewhat noisier than the MRI CBF map. Weinvestigated possible regional differences in CBF maps obtained by thetwo methods. These appeared to be mainly associated with either noiseartifacts or the presence of veins in the PET image slice. Noise in PETimages appears as ‘streaky artifacts’ that sometimes propagate into theCBF maps. Veins, on the other hand, are often interpreted by the kineticmodel in equation 13 as a high flow region, whereas they are rarelydetected by the MR sequence.

FIG. 2 shows plots of regional CBF values with their standard deviationsfor individual pigs. Notice that normo- as well as hypercapnic datapoints are plotted in the same diagram to visualize overall agreement ofabsolute values as well as responses to CO₂ among PET and MRI. There wasa tendency for normocapnic data points to be grouped in the lower leftand hypercapnic data points in the upper right quadrant of the plots.Notice that the error bars associated with the MRI measurements appearsmaller than the corresponding PET values for the same region Theaverage standard deviation on regional flow estimates was on the average30% smaller than the corresponding standard deviation for the same PETROI. FIG. 3 shows the corresponding plot for repeated PET measurement ofCBF with ¹⁵O butanol. The results of the linear regression analysis areshown in Table 2. The slopes of the linear regression lines did notsignificantly differ among the pigs (by multiple pairwise t-tests). Formost animals, the regression coefficient r² (the proportion of thevariance accounted for by the regression) ranged between 0.7 and 0.8.

This was slightly lower than the value (i.e. 0.86) obtained by comparingCBF maps obtained in identical brain slices with PET. Hence, theadditional inaccuracies introduced by comparing CBF determined by twodifferent methods are therefore small compared with the varianceassociated with comparisons made within the same method.

TABLE 2 Pig a b r² 1 0.82 ± 0.10 11 ± 5 0.79 2 1.00 ± 0.11 −2 ± 6 0.81 30.99 ± 0.15  0 ± 10 0.70 4 0.97 ± 0.11 −4 ± 6 0.79 5 0.98 ± 0.11  2 ± 70.81 6 0.90 ± 0.12  6 ± 5 0.75 6* 0.77 ± 0.07 10 ± 3 0.86

FIG. 4 shows CBV maps obtained with MR and PET, respectively. As CBV andCBF are obtained in the same units, absolute CBV values were obtained bymultiplying the integrated value by the normalisation factor Φ_(Gd)=1.09determined above. FIG. 5 plots average absolute MR versus PET values ofCBV for corresponding slices under normo- and hypercapnia in 6 pigs.Care was taken to include brain parenchyma rather than large vessels inthe image. Also shown is the linear regression line with slope 0.45±0.11(SD) and y intercept −0.56±0.61 (SD). Notice the apparent linearitybetween vascular volume measurements with PET and MRI. As both MR andPET CBV values are now in absolute values, the plot shows that only 40%of the total vascular volume is detected by the spin echo EPI MRtechnique.

Discussion

In spite of the inherent complexity of susceptibility contrastmechanisms and its use for measurements of CBF, our rather simpleapproach to quantify CBF from MRI seems promising as a first approachtowards measurement of absolute CBF. In five out of six animals, thecommon conversion factor yielded absolute CBF values in agreement withthose obtained by PET. Furthermore, the MRI technique yielded CBF mapswith good contrast between gray and white matter structures, just as byregional comparison, MRI CBF maps had less noise than the correspondingPET CBF maps, using similar spatial resolution. In the following, wewill discuss how our assumptions and experimental approach may explainthe poorer correlation between MRI and PET CBF results than amongrepeated PET CBF measurements.

First, assuming a common constant that relates injected MR contrast doseto the area under the image-based arterial input concentration timecurve may not always hold true. The validity of this assumption issensitive to the fraction of the injected contrast dose delivered to thebrain circulation in the two experimental conditions, and moreimportantly, the linearity between contrast concentration and change intransverse relaxation rate assumed in equation 15. Secondly, we assumeda linear relationship between CBF and arterial CO₂ levels whencorrecting for different degrees of hypercapnia in PET and MRIexperiments. Deviations from linearity may, however, cause systematicchanges in the slope and intercept of the regression line, just as theCO₂ response of the animal may change after long-term anesthesia (MRmeasurements were performed approximately 4 hours after the PETmeasurements).

As for more methodological problems, comparing MRI with PET may haveaffected our regression results in several ways. Co-registration of MRIand PET data may not be completely accurate, just as MR images obtainedwith echo planar imaging can be somewhat distorted due to magnetic fieldinhomogeneities and susceptibility artifacts. The latter causesanatomical structures imaged by the EPI sequence not to be imaged in theexact location as in the 3D image sequence used for co-registration. Incases where we noticed slight in-plane differences in locations, weadjusted the location of the ROI in the MRI images to account for thisfact.

A more complex problem was caused by the differences in inherentresolutions of PET and MRI. For our PET tomograph, the effectiveresolution with the parameters used is approximately 4.5 mm in thecenter of the investigated volume. By using a Gaussian filter, we soughtto blur the MRI measurements to yield the same resolution as the PET CBFmeasurements. However, the CBF images in FIG. 1 still indicate thatthere may be differences in resolution that are not accounted for,causing influence from neighbouring regions to be different in the twoimaging modalities, thereby causing a non-linear relationship betweenregional CBF values simply due to differences in resolution. We believethese factors explain the slightly better regression statistics obtainedwhen comparing two PET CBF measurements rather than comparing MR.

Some data sets (pig 1 and 6) yielded regression lines with slopessomewhat below unity and a positive y-axis intercept, as also found whencomparing ¹⁵O water and ¹⁵O butanol CBF measurements. With the lattertracer, the discrepancy is due to limited diffusibility of water acrossthe blood-brain barrier, causing higher flows to be underestimated (Ohtaet al., 1996). For MRI measurements, the earlier simulation studies alsopredicted that high flow rates would be underestimated, when themicrovascular mean transit time is short relative to the characteristictime scales of the bolus input and the imaging rate underestimated(Østergaard et al., 1996). By very rapid bolus administration andimaging once per second, we hoped to minimise this effect. The resultsindicate that the MR technique may perform slightly worse than the PETmethod with ¹⁵O water in terms of measuring very high flow rates.

The measurements provide insight into the selectivity for the effect ofsmall vessels of the T₂-weighted spin echo EPI sequence used in ourexperiment. By a Monte Carlo simulation approach, Weisskoff et al.(1994) previously demonstrated that the susceptibility contrast in thisimaging sequence arises mainly in small, capillary size vessels. As thedistribution of fractional vascular volume as a function of vasculardiameter is not fully known, it is difficult to predict absolute volumevalues based on these simulations. Our 40–50% estimate of the vascularfraction detected by MR is therefore difficult to compare to theoreticalpredictions. However, studies of peripheral tissue indicate that vesselssmaller than 3040 μm diameter (small arteries, arterioles, capillaries,venules and small veins) represent roughly 50% of the total vascularvolume (Johnson, 1973). Assuming that the MR measurements arepredominantly sensitive to the smallest vessels, our value of 40–50%therefore points towards a sensitivity to vessels smaller than 30–40 μm.of the MR technique. This in turn makes the CBF and CBV techniquessensitive to microvascular phenomenons, e.g. neovascularization inneoplasia (Aronen et al., 1994) and flow-volume mismatches in stroke dueto delayed passage through oxygen exchanging vessels (Heiss et al.1994).

EXAMPLE 2

Cerebral Blood Flow Measurements by MRI Bolus Tracking: Comparison with[¹⁵O]H₂O Pet in Humans

SUMMARY OF THE EXAMPLE

In six young, healthy volunteers, a novel method to determine cerebralblood flow (CBF) using magnetic resonance (MR) bolus tracking wascompared with H₂ ¹⁵O positron emission tomography (PET). The methodyielded parametric CBF images with tissue contrast in good agreementwith parametric PET CBF images. Introducing a common conversion factor,MR CBF values could be converted into absolute flow rates, allowingcomparison of CBF values among normal subjects.

Background

Recent results indicate that it may be possible to measure cerebralblood flow (CBF) by dynamic magnetic resonance imaging (MRI) ofparamagnetic contrast agent bolus passage (Østergaard et al., 1996a).Due to the complexity of suceptibility contrast, this techniqueinitially only allowed determination of relative flow rates. In apreliminary study in six normal volunteers, the mean gray:white flowratio was found to be in good agreement with PET literature values forage matched subjects (Østergaard et al., 1996b). In a recent animalhypercapnia study (Østergaard et al., 1997), an approach was introducedto allow absolute quantitation by introduction of an empiricalnormalisation constant.

In this study we compare absolute regional NMR bolus CBF values with CBFvalues determined by [¹⁵O] water uptake, detected by positron emissiontomography (PET) in normal human volunteers.

Theory

MRI CBF Measurements

Estimation of cerebral blood flow from measurement of non-diffusabletracers is discussed in detail by Østergaard et al. (1996a). In brief,the concentration C_(t)(t) of intravascular contrast agent within agiven tissue element can be writtenC _(t)(t)=f ₁ ·C _(a)(t){circle around (×)}R(t)  Eq. 16where F_(t) is tissue flow and {circle around (×)} denotes theconvolution of R(t), the vascular residue function (normalised impulseresponse function) with the arterial input function, C_(a)(t).

It has been demonstrated that, using singular value decomposition (SVD),R(t) and CBF can be determined with good accuracy, independent of theunderlying vascular structure and volume (Østergaard et al., 1996a).

PET CBF Measurement

The regional uptake of water is described by the model of Ohta (Ohta etal. 1996):

$\begin{matrix}{{C_{br}(t)} = {{\left( {1 - V_{p}} \right) \cdot K_{1} \cdot {\int_{0}^{t}{{C_{a}(\tau)}e^{- {k_{2}{({t - \tau})}}}{\mathbb{d}\tau}}}} + {V_{p} \cdot {C_{a}(t)}}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$where we assume K₁=CBF for water, and

${k_{2} = \frac{K_{1}}{V_{d}}},$where V_(d) is the distribution volume of the tracer. V_(p) is theinstantaneous vascular distribution volume of the tissue.Material and MethodsVolunteers and Experimental Protocol

Six young, healthy volunteers (3 male, 3 female, mean age 26±6 years)were examined. Two additional volunteers were included in the study. Onewas excluded due to head motion during MRI measurements, while the otherwas excluded due to a significant change (>5%) in P_(a)CO₂ in betweenPET and MR scans. PET and MR scans were performed on the same day,within 2 hours of each other. Prior to the examination, arterial andvenous catheters were inserted in the left radial artery and rightantecubital vein, respectively. Arterial blood samples were withdrawnand analysed (ABL 300, Radiometer, Copenhagen) at regular intervals tomonitor blood gases and whole blood acid-base parameters (pH, pCO₂, pO₂,HCO₃ and O₂ saturation). Prior to each CBF measurement, the volunteerwas allowed to rest at least 30 minutes with closed eyes. The projectwas approved by the Regional Danish Committee for Ethics in MedicalResearch, and performed after informed, written consent from eachvolunteer.

PET Imaging Protocol.

The volunteers were studied in a Siemens ECAT EXACT HR PET camera usinga custom-made head-holding device. To measure CBF, a fast i.v. bolusinjection of 500 MBq H₂ ¹⁵O in 5 ml saline was performed, followedimmediately by an i.v. injection of 10 ml of isotonic saline to flushthe catheter. A sequence of nineteen (12, 6 and 3 samples during thefirst, second and third minute, respectively) arterial blood samples(1–2 ml) and 12 PET brain images (6, 4 and 2 images per minute,respectively) were then obtained. Brain image data were reconstructedusing scatter correction, and a Hann filter with a cutoff frequency of0.5 pixel⁻¹, resulting in an isotropic spatial resolution (FWHM) of 4.6mm. Correction for tissue attenuation was based on a ⁶⁸Ga transmissionscan. Radioactivity levels in image and arterial blood were correctedfor the half-life of ¹⁵O (123 s).

Pet Radiochemistry

¹⁵O₂ was produced by the ¹⁴N(d,n)¹⁵O nuclear reaction by the bombardmentof nitrogen gas with 8.4 MeV deuterons using a GE PETtrace 200cyclotron. ¹⁵O₂ was mixed with hydrogen and passed in a stream ofnitrogen gas over a palladium catalyst at 150° C. to produce ¹⁵O-watervapour, which was trapped in 10 ml sterile saline.

MRI Imaging Protocol

MR imaging was performed using a GE Signa 1.0 Tesla imager (GE MedicalSystems, Milwaukee, Wis.). Following a sagittal scout, a T₁ weighted 3Dimage was acquired for co-registration of MR and PET data. For dynamicimaging of the bolus passages, spin echo (SE) echo planar imaging (EPI)was performed (Repetition time TR=1000 ms, echo time TE=75 ms), using a64 by 64 acquisition matrix was used with a 18 by 18 cm transverse FOV,leading to an in-plane resolution of 3 by 3 mm. The slice thickness was6 mm. In all experiments, bolus injection of 0.2 mmol/kg Gadodiamide(OMNISCAN®, Nycomed Imaging, Oslo, Norway) was performed at a rate of 5ml/sec. A pre-dose of 0.05 mmol/kg was given to reduce systematiceffects from changes in blood T₁.

MR Image Analysis

To determine tissue and arterial tracer levels C(t), we usedsusceptibility contrast (Villringer et al., 1988) arising fromcompartmentalisation of the paramagnetic contrast agent. We assumed alinear relationship (Weisskoff et al., 1994) between paramagneticcontrast agent concentration and the change in transverse relaxationrate ΔR₂:

$\begin{matrix}{{{C(t)} \propto {\Delta\;{R_{2}(t)}}} = {{- {\log\left( \frac{S(t)}{S(0)} \right)}}/{TE}}} & {{Eq}.\mspace{14mu} 18}\end{matrix}$where S(O) and S(t) are the signal intensities at the baseline and attime t, respectively, and TE the echo time. The arterial concentrationwas determined from pixels around the middle cerebral artery in theimaging plane (Porkka et al., 1991). The integrated area of the arterialinput curve was in each measurement normalised to the injected contrastdose (in mmol per kg body weight) according to our earlier approach(Østergaard et al., 1997). Deconvolution was performed following theapplication of a 3×3 uniform smoothing kernel to the raw image data, andthe maximum point on the deconvolved impulse response curve was chosento be CBF.PET Image Analysis

The 3D PET CBF images were used to automatically co-registered with the3D MR images (Collins et al., 1994). Raw PET image data were thentransformed and re-sampled to the same spatial location and resolutionas the MR CBF data to allow direct comparison of the two techniques.Following the application of a 3×3 uniform smoothing kernel to our rawPET image data, these were fitted to equation 2 using non-linear, leastsquared regression analysis on a pixel-by-pixel basis.

Comparison of PET and MR Parametric Images

Pixel by pixel maps of CBF (at similar anatomical locations, pixel sizeand resolution) generated by PET and MR, respectively, were thencompared on a regional basis. In each image, 20–25 regions of similarsize were chosen, including gray and white matter. The means of allregional values were then averaged, to yield a common conversion factorbetween MRI flow units and absolute flow in ml/100 ml/min). Regionalaverage CBF values and their standard deviations (derived from thepopulation of pixels within the ROI) were then compared.

Results

Table 3 shows values of P_(a)CO₂ and P_(a)O₂ for all volunteers duringMR and PET measurements. Volunteer 3 showed a 13% change in P_(a)CO₂ andwas excluded from the analysis, while volunteer 1 had to be excluded dueto head motion during the MR measurements.

TABLE 3 Subject P_(a)CO₂ (kPa) P_(a)O₂ (kPa) no PET MR % change PET MR %change 1 5.97 5.63 −5.7 12.11 13.45 4.8 2 5.49 5.35 −2.5 15.815 16.3953.7 3 6.63 5.79 −12.7 12.05 12.625 4.8 4 5.31 5.33 0.4 15.58 16.165 3.85 5.25 5.325 1.4 17.175 15.265 −11 6 4.92 4.93 0.2 15.165 14.67 −3 74.485 4.675 4.2 15.925 16.97 6.6 8 4.965 4.965 0 16.16 15.205 −5.9

By averaging all regional flow rates, a common conversion factor,Φ_(Gd)=0.87 was found. In the following, all MR flow rates weremultiplied by this constant.

FIG. 6 shows parametric CBF maps determined by PET and NMR,respectively. To facilitate visual comparison, the MR flow image wasblurred to the resolution of the PET image. Also shown is thecorresponding anatomical MR image. It is noticed that vessels appear tobe treated somewhat differently by the two methods: In the PET images,these appear as high flow areas, whereas in the MR images, arterialbranches appear as high flow regions. FIG. 6 shows MR versus PET plotsof regional CBF values along with their standard deviations for the sixvolunteers. Also shown are linear regression lines and their 95%confidence regions. White matter ROIs are represented in the lower leftquadrant of the plots, whereas gray matter ROIs are in the upper right.There was no systematic deviation from the regression lines for gray andwhite matter flow rates, in agreement with the qualitative appearance ofthe flow maps in FIG. 6. Also, notice that error bars are of comparablesize for PET and MR for identical size ROIs. Table 4 shows theregression results. The portion of the variance accounted for by theregression (r²), was generally between 65 and 83 percent (see Table 4).To test whether the differences in regression slopes could be ascribedto individual uncertainties, the F statistic was calculated, showing nosignificant differences. Still, it was noticed that subject 5 had asomewhat larger slope than the remaining volunteers. In one volunteer(subject 8), we found an apparent hypoperfusion in the occipital lobenot visible in the PET CBF image (FIG. 8). We will discuss theimplications of this below.

TABLE 4 Subject Slope (m_(i) ± s_(i)) Intercept r² 2 1.09 ± 0.17    6.88± 5.17 0.65 4 1.08 ± 0.14  −0.48 ± 3.58 0.77 5 1.34 ± 0.17  −6.84 ± 4.210.74 6 1.01 ± 0.10 −10.86 ± 5.92 0.83 7 1.12 ± 0.12    1.73 ± 3.29 0.798 0.94 ± 0.14    2.41 ± 6.42 0.66 Mean 1.10 ± 0.14  −1.19 ± 6.51 0.74Discussion

There was generally good agreement between regional PET and MR CBFvalues. The fact that the ratio of gray and white matter flow ratesappears identical using MR and PET confirms the earlier finding thatrelative CBF values can be determined within the same subject(Østergaard et al., 1996b). Furthermore, the data supports that ourearlier normalisation routine (Østergaard et al., 1997) allowsdetermination of absolute flow rates and hence comparison amongsubjects. The conversion factor found (0.84) was somewhat lower thanthat previously found for pigs (1.09) (Østergaard et al., 1997). Weascribe this to anatomical differences, especially the fact that theportion of the cardiac output distributed to the brain is probablysmaller in pigs than in humans.

The variance observed relative to a simple linear relationship betweenthe two different CBF estimates can be ascribed to several factors.First, CBF measurements were performed about 2 hours apart, and eventhough the arterial CO₂ levels were nearly identical, changes in theoverall level of consciousness may have resulted in different flowrates. Also, as regional flow is unlikely to be constant over even veryshort time scales, the fact that the MR CBF measurements are acquired inonly 15 seconds, whereas radiolabeled water levels are observed forthree minutes by PET, may contribute to differences in regional values.More technical and methodological issues may have affected ourmeasurements, as well. First, the rapid EPI sequence used in ourmeasurements is sensitive to magnetic field inhomogeneities. This mayresult in misregistration of corresponding PET and MRI regions. This isillustrated in FIG. 8, displaying the conventional MRI as well as thePET CBF maps from the volunteer 6. FIG. 8 also shows what may reflect amethodological problem of the MR technique. The MR technique issensitive to large delays in tracer arrival, causing CBF to be somewhatunderestimated. In this volunteer, the tracer arrival in the posteriorcirculation was delayed by several seconds relative to the remainingbrain. This, apart from possible differences in visual activity duringthe two measurements, may explain the occipital hypoperfusion in thisvolunteer. Finally, the assumption that the area under the arterialconcentration time curve is proportional to the injected dose in allsubjects may not hold true under all circumstances. Also, circulatorydisturbances may cause the characteristic time scale of the arterialinput to become longer than that of the vascular transit time, makingCBF measurements difficult (Kent et al 1997). This underlines theimportance of performing very rapid bolus inputs, and validating thisapproach in patient populations, especially those with eithercirculatory disturbances or delayed tracer arrival in the brain (seeabove), e.g. major artery occlusion.

There were some qualitative differences among the CBF images obtained bythe two modalities. The MR technique was found to interpret smallarteries as high flow regions. This is inherent to the technique, as itdoes not mathematically distinguish between large vessel and capillarytracer dispersion. However, as CBV is simultaneously determined byintegration of the tissue concentration time curve (Rosen et al. 1991),this does not pose a problem in interpreting the CBF maps. Also, due tothe inherent sensitivity of susceptibility contrast imaging to smallvessels (Fisel et at. 1991, Weisskoff et al. 1994) large vessels are notseen in the images. In contrast, PET CBF images partly interpretdispersed venous blood as tissue flow, whereas arteries are suppressedby means of the V₀ term in equation 17.

In one volunteer (subject 8), we found a marked hypoperfusion in theoccipital lobe possibly due to delay in the arrival of tracer in theposterior circulation. This effect was predicted in theoreticalsimulations of the technique (Østergaard et al. 1996a). FIG. 9 shows howflow estimates become increasingly underestimated as the arrival delayof the tracer at a brain region increases, in both PET and MR CBFmeasurements (Simulations were performed by simply introducing delaysbetween the arterial and cerebral concentration time curves in volunteer6). Notice, however, that whereas PET measurements may underestimateflow by 15%, underestimation by MRI can be as much as 50%. Even thoughwe only noticed this effect in one volunteer, these simulationsunderline the importance of further evaluating this technique in patientpopulations with e.g. vascular diseases. Also, we are currently workingon approaches to minimise the sensitivity of our CBF algorithm to tracerarrival delays.

We used rather low spatial resolution (64 by 64 matrix), single slicemeasurements. It is worth noticing that most current MR systems with EPIcapabilities allows multi-slice acquisitions at a considerably higherspatial resolution (typically 2.5 by 2.5 mm pixels). This allows CBFmeasurements at twice the spatial resolution of most current PETsystems.

Conclusion

The study indicates that relative as well as absolute CBF values can bedetermined using MRI bolus tracking in humans. Although furthertheoretical and experimental validation is needed in patients, thetechnique provides easy, rapid CBF measurement without invasive arterialmeasurements or radioactive exposure, at high spatial resolution.

EXAMPLE 3

Modeling Cerebral Blood Flow and Flow Heterogeneity from MagneticResonance Residue Data

Summary of the Example

Existing model-free approaches to determine cerebral blood flow byexternal residue detection show a marked dependence of flow estimates ontracer arrival delays and dispersion. In theory, this dependence can becircumvented by applying a specific model of vascular transport andtissue flow heterogeneity. A method is presented to determine flowheterogeneity by MR residue detection of a plasma marker. Probabilitydensity functions of relative flows measured in 6 healthy volunteerswere similar among tissue types and volunteers, and were in qualitativeagreement with literature measurements of capillary red blood cell andplasma velocities. Combining the measured flow distribution with a modelof vascular transport yielded excellent model fits to experimentalresidue data. Fitted gray:white flow rate ratios were in good agreementwith PET literature values, as well as a model-free singular valuedecomposition (SVD) method in the same subjects. The vascular model wasfound somewhat sensitive to data noise, but showed far less dependenceupon vascular delay and dispersion than the model-free SVD approach.

Background

A technique to determine cerebral blood flow (CBF) by magnetic resonance(MR) bolus tracking of an intravascular contrast bolus has recently beenpresented (Østergaard 1996a). By performing non-parametric singularvalue decomposition (SVD) deconvolution of tissue time concentrationcurves by a non-invasively determined arterial input function, thealgorithm (hereafter referred to as the SVD method) generatespixel-by-pixel maps of CBF (Østergaard 1996a). The SVD method has beendemonstrated to yield CBF values in excellent agreement with PET innormal volunteers (Example 2 (Østergaard 1998a)), as well as in ananimal hypercapnia model (Example 1 (Østergaard 1998b)). Although themodel-free SVD method offers the advantage of being independent of theunderlying vascular structure, the method is somewhat susceptible todispersion and delay of the measured AIF before it reaches the imagingpixel (Østergaard 1996b). Especially in the setting of major vesseldisease, dispersion in the feeding vessel may be significant relative totissue tracer retention, causing underestimation of CBF, and thereforeoverestimation of the CBV:CBF ratio (Østergaard 1996b). This ratio, theplasma mean transit time (MTT), is an important parameter in evaluatingcerebrovascular perfusion reserve, and therefore the inability of theSVD approach to distinguish vascular dispersion from prolonged tissueMTT may ultimately impair its clinical use.

Bassingthwaighte and co-workers have developed modelling tools todescribe major vessel transport as well as microvascular tracerretention (King 1993; King 1996) A derived model of the coronarycirculation has been successfully applied to MR data, allowingnon-invasive measurements of coronary blood flow (Kroll 1996). Thismodel (hereafter referred to as the vascular model), modified for thecerebral circulation, may ultimately provide estimates of CBF and MTTindependent of major vessel delay and dispersion. The aim of this studywas to extend this vascular model to the cerebral circulation. First, afirst-order expression of flow heterogeneity in the cerebral circulationwas derived by a model-free analysis of tracer retention in areas ofnegligible major vessel dispersion. To validate the model, the vascularmodel was fitted with measured flow heterogeneity, to human MR residuemeasurements, and compare the resulting flow rates to literature values,as well as the SVD method. Finally, the sensitivity of the vascularmodel to tracer delays was compared in simulated data.

Theory

Vascular Model

A modified version of the vascular model previously described by Krollet al (Kroll 1996) was used. The vasculature was modelled a major,feeding artery in series with 20 small vessels in parallel—See FIG. 10.In the vascular model the flow is directed along the parallel pathways,with w_(i) representing the fraction of flows with values f_(i)·Fp,where F_(p) is total flow. The feeding artery was described by a fixed,relative dispersion in transit times (RD=0.48) and a delay, determinedby its volume fraction, V_(art) (King 1993). The capillaries weremodelled as simple delay lines of fixed length (100 μm), with volumeV_(p). In the following, the tissue flow F_(p), the feeding vascularvolume V_(art), and capillary volume V_(p) was allowed to vary. Theobserved signal changes due to magnetic susceptibility contrast agentarises—when using a spin echo sequence (See Materials and Methodsbelow)—mainly from capillaries (Fisel 1991; Boxerman 1995; Weisskoff1994). In the model, total tissue tracer concentrations were thereforecalculated based on the amount of tracer in the small, parallel vessels.The distribution of transit times in the capillary bed was incorporatedby an algorithm assigning appropriate flows and weights to the parallelvascular paths, to achieve a given heterogeneity (King 1996). This flowheterogeneity is described by a probability density function (PDF),assigning a probability w(f) to a given relative flow f, i.e. flowrelative to the mean flow, F_(p). In the following, it is described howan estimate of flow heterogeneity in humans is obtained from MR residuedata. For a more detailed discussion of modelling flow heterogenity, seeKing et al. (King 1996).

Flow Heterogeneity from Residue Data

The fact that the impulse response to a plasma tracer can be estimatedby nonparametric deconvolution of the tissue residue during the tracerpassage by a non-invasively determined arterial input function (AIF) isutilised. From this the distribution of plasma transit times, and—undercertain assumptions regarding the distribution of capillary lengths—thedistribution of flows in the region are derived.

The tissue concentration C_(t)(t) of tracer in response to an arterialinput function C_(a)(t) is given in Equation 4. The formula isequivalent to the integral

$\begin{matrix}{{C_{t}(t)} = {{F_{t} \cdot {{C_{a}(t)} \otimes {R(t)}}} \equiv {F_{t} \cdot {\int_{0}^{t}{{C_{a}(\tau)}{R\left( {t - \tau} \right)}{\mathbb{d}\tau}}}}}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$where F_(t) is tissue flow and R is the residue function, i.e. thefraction of tracer present in the vasculature at time t after a perfect,infinitely sharp input in the feeding vessel. Assuming the arterial andcerebral concentrations are measured at equally spaced time-points t₁,t₂, . . . , t_(N), this equation can be discretized, assuming that overshort time intervals Δt, the residue function and arterial input valuesare constant in time:

$\begin{matrix}{{C_{t}\left( t_{j} \right)} = {{F_{t} \cdot {\int_{0}^{t_{j}}{{C_{a}(\tau)}{R\left( {t - \tau} \right)}{\mathbb{d}\tau}}}} \approx {\Delta\;{t \cdot F_{t} \cdot {\sum\limits_{i = 0}^{j}{{C_{a}\left( t_{j} \right)}{R\left( {t_{j} - t_{i}} \right)}}}}}}} & {{Eq}.\mspace{14mu} 20}\end{matrix}$which is equal to the expression in Equation 6.

As previously described (Østergaard 1996b), this equation can bemodified to residue and arterial input functions that vary linearily intime. The SVD approach provides a powerful numerical tool to solveEquation 6 in the presence of experimental noise to yield the residuefunction. The distribution of transit times, h(t), is then found from

$\begin{matrix}{\left. {{R(t)} \equiv \left\lbrack {1 - {\int_{0}^{t}{{h(\tau)}{\mathbb{d}\tau}}}} \right\rbrack}\Rightarrow{h(t)} \right. = {- \frac{\mathbb{d}R}{\mathbb{d}t}}} & {{Eq}.\mspace{14mu} 21}\end{matrix}$i.e. the slope of the residue function. At a given time point t₁, h(t)can be estimated as

$\begin{matrix}{{h\left( t_{i} \right)} = {\frac{1}{2} \cdot \left( \frac{{R\left( t_{i + 1} \right)} - {R\left( t_{i - 1} \right)}}{\Delta\; t} \right)}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

The probability density function (PDF) of transit times (t) is turnedinto a distribution of relative flow rates f, w(f), by requiringw(f)df=h(t)dt  Eq. 23and that the central volume theorem (Stewart 1894) is obeyed (Equation7). Assuming all vascular paths have equal volume, the distribution offlow rates is obtained from Equation 8, and normalised to have unit meanflow and area (Equation 9).Materials and MethodsVolunteer Data

Six normal volunteers (Age 29±4 yrs) were examined according to astandard perfusion protocol on a GE Signa 1.5 T imager (GeneralElectric, Waukesha, Wis.) retrofitted for EPI capabilities (Instascan,Advanced NMR Systems, Wilmington, Mass.), using spin echo (SE), echoplanar imaging (EPI) with a time of repetition (TR) of 1.0 seconds, anda time of echo (TE) of 100 ms. The slice thickness was 5 mm with anin-plane resolution of 1.6 mm by 1.6 mm in a 40 by 20 cm field-of-view(FOV). A total of 52 images were acquired, starting 15 seconds beforei.v. injection of 0.3 mmol/kg contrast medium (Dysprosium-diamide,Nycomed Imaging, Oslo, Norway). Intravascular contrast agentconcentrations, C(t), were estimated assuming a linear relationshipbetween concentration and change in transverse relaxation rate, ΔR₂(Villringer 1988; Weisskoff 1994) (Equation 1).

Feeding arterial branches were identified in the image slice as pixelsdisplaying early concentration increase after contrast injection (Porkka1991). This approach does not determine absolute arterial tracer levels,but provides the shape of the AIF. To standardise the analysis below,the arterial input function was therefore scaled to yield a mean CBV of3% (Example 1 (Østergaard 1998b)). In volunteers, a single arterialinput function in the imaging plane was used for all tissue regions.

Determination of Flow Heterogeneity

Tissue concentration time curves were formed using Equation 1. Threegray and two white matter tissue regions consisting of 4 image pixels(0.05 cc) were then chosen, based on cerebral blood volume maps (Rosen1990). The tissue residue function was calculated by SVD deconvolutionof the tissue concentration time curve with the AIF. The resultingresidue function was then converted into a probability density function(PDF) of relative flows as described in the Theory section above

Model Analysis

The experimentally determined flow heterogeneity PDF was then enteredinto the vascular model described above. For sixteen gray and whitematter regions (0.25–0.4 cc), F_(p), V_(p), and V_(art) were adjusted toobtain optimal fits to the corresponding tissue concentration timecurves by nonlinear regression analysis (Chan 1993). The initialconditions were F_(p)=40 ml/100 ml/min, V_(p)=2%, and V_(art)=0.1%. Theremaining model parameters are given in FIG. 10.

Comparison with Model-Free Approach

To compare the flow rates obtained with the vascular model with those ofthe model-free SVD approach (Østergaard et al., 1996a), the height ofthe deconvolved tissue response curve (F_(t)·R(t_(i)) in Equation 3),was determined for the same regions as used in the model analysis above.After determining mean white matter flow rate, 9 relative gray:whiteflow ratios were calculated for each volunteer, and compared with thoseobtained by the vascular model.

Sensitivity to Tracer Delays

In volunteer 4, each pixel tissue concentration time curve was delayedin steps of 0.25 second by linear interpolation to simulate the effectsof tracer arrival delays. The simulated image data were then analysed asdescribed above, and fitted flow rates by the SVD and vascular modelapproach plotted as a function of delay for comparison.

Sensitivity to Noise and Initial Conditions

To determine the overall sensitivity of parameter estimates with thevascular model to experimental noise, a set of synthetic data sets weregenerated using the vascular model itself, and two sets of typicalvalues for flow, volume, and feeding artery volume (F_(p)=20 ml/100ml/min, V_(p)=2%, V_(art)=0.5%, and F_(p)=50 ml/100 ml/min, V_(p)=3%,V_(art)=0.5%). These were converted into a MR signal intensity timecurve using Equation 1, to generate a typical signal loss (25% for graymatter, equivalent to the higher flow) during a bolus passage. Randomgaussian noise was then added, and ‘noisy’ concentration time curves ereagain calculated from Equation 1. Simulated SNRs varied from 400 down to12, the latter being typical for raw, pixel-by-pixel data obtained withperfusion protocols on a clinical MR system. The synthetic curves wereanalysed using the vascular model, using two different sets of initialconditions. These were chosen to represent two extremes of physiologicalvalues: F_(p)=80 ml/100 ml/min, V_(p)=6%, V_(art)=1%, and F_(p)=20ml/100 ml/min, V_(p)=2%, V_(art)=0.1%. For each SNR, 24 simulations wereperformed, and the mean and standard deviations of the fitted modelparameters were calculated for further evaluation. The dependency oninitial conditions was evaluated by recording the number of simulationswhere two different initial conditions caused resulting fittedparameters to differ by more than 10% from their mean. To comparestability of the vascular model and SVD method to experimental noise,flow rates were determined from the same synthetic curves by the SVDmethod.

Results

FIG. 11 shows a set of typical tissue and arterial concentration timecurves obtained from volunteer 1. The tissue ROIs consisted of 25–35pixels (corresponding to 0.3–0.4 cc volumes). The average signal tonoise ratio (SNR) (defined as the maximum tissue R₂ increase duringbolus passage divided by the standard deviation of the noise relative topre-bolus baseline image intensity) for the tissue volumes used formodel validation (0.25–0.4 cc) was 30. The SNR of gray matter was afactor of 2 to 3 higher than that of white matter, due to the higherblood volume.

Flow Heterogeneity

FIG. 12 shows the location and size of three regions chosen fordetermination of flow heterogeneity in volunteer 4. The regions areoverlaid on a CBF map calculated by the SVD-method to illustrate thecontrast and spatial resolution of the techniques. Also shown are thecorresponding flow heterogeneity plots derived from the three regions.The transit time and derived flow heterogeneity PDFs were found to beremarkably similar among regions and among volunteers. FIG. 13 a showsall pairs of relative transit time t and corresponding h(t) measured forall regions in all 6 volunteers. FIG. 13 b shows—under the assumption ofequal capillary lengths—the corresponding plot of relative flow f andw(f) measured for all regions and volunteers. Due to this constancyacross regions and subjects, the (f,w(f)) points were consequentlyaveraged into 30 points (Full curve) and used as a global expression forflow heterogeneity in normal tissue in the subsequent model analysis.The parameterised w(f) is given in Table 1. The distribution of flows ismarkedly right-skewed, with the majority of capiliaries having flowrates less than the mean flow. The maximum probability is reached atroughly ⅔ of the mean flow.

Model Validation

In the following, the experimentally determined flow heterogeneity PDFwas applied, and the vascular transport is therefore described by onlythree parameters, V_(art), F_(p) and V_(p). FIG. 14 shows a typical setof tissue concentration time curves as well as the fits provided by themodel (Basal ganglia: CBF=60.3±1.0 (SE) ml/100 ml/min, Gray matter:CBF=48.5±1.2 ml/100 ml/min, white matter: CBF=19.5±0.8 ml/100 ml/min).Notice the model takes into account the observed earlier tracer arrivalin tissue with higher flow rates. The quality of model fits toexperimental data shown in FIG. 14 is typical for the patients examined.Table 5 shows the mean gray:white matter flow ratios for 8 regions. Themean gray:white flow ratio was 2.89±0.35 with the vascular model.

TABLE 5 Regional gray:white flow ratios in 6 volunteers Volunteer no.Region 1 2 3 4 5 6 Average Basal ganglia left 4.19 3.41 3.70 2.73 3.763.39 3.53 right 3.76 3.41 2.99 2.80 3.66 3.86 3.41 Frontal medial left2.89 2.91 1.94 2.32 2.55 2.03 2.44 right 2.66 2.73 3.6 2.24 3.06 3.032.88 Temporal left 3.55 3.16 3.14 2.55 4.31 2.29 3.16 right 4.52 3.593.27 2.02 3.71 2.78 3.31 Occ.-temporal left 2.50 2.37 2.66 2.20 2.552.74 2.50 right 2.78 2.05 3.70 2.08 1.70 1.97 2.38 Occ. medial left 3.602.87 2.27 2.06 2.30 2.84 2.66 right 2.95 2.12 3.57 2.17 2.15 2.43 2.57Average 3.34 2.86 3.08 2.31 2.97 2.74 2.89Comparison with Model-Free Approach

FIG. 15 shows gray:white matter flow ratios determined by the modelapproach plotted versus corresponding ratios in identical regionsdetermined by the SVD approach. The three volunteers were chosen basedon a significant spread in individual, regional gray:white matterratios, in order to facilitate comparison between approaches. In thefigure, linear regression lines for each volunteer are shown (Volunteer1: y=1.02+0.21 (r²=0.75), Volunteer 2: y=1.16x−0.68 (r²=0.91), Volunteer5: y=0.95x−0.72 (r²=0.95)). The line of identity was within the 95%confidence intervals of a common linear fit. Notice regional gray:whitematter ratios using the two techniques all lie near the line ofidentity.

Sensitivity to Tracer Arrival Delays

FIG. 16 a shows the effect of AIF delay on fitted flow rates for thevascular model and the SVD approach, respectively. The gray and whitematter tissue ROIs consisted of 90 image pixels (1.1 cc). Vascular modeland SVD values were obtained from identical regions. The SVD approachprogressively underestimates flow rates with tracer arrival delay. Therelative underestimation is roughly proportional to the delay, reaching25% for white matter and 35% for gray matter at a delay of 3 seconds,respectively. For the model approach, flow estimates are remarkablyindependent of delay FIG. 16 b shows the fitted feeding artery volume asa function of delay. The vascular model interprets increasing delays asincreased feeding vessel volume in accordance with the definition of thevascular operator. As vascular dispersion is a priori unknown in actualmeasurements, fitting was performed assuming a vascular dispersionRD=0.48, although the delay was simulated to be dispersion-less Noticefluctuations of fitted flow values around 1 is accompanied byfluctuations of the fitted vascular volumes. These fluctuations and thetendency of flow and vascular volume to co-vary are discussed furtherbelow.

Sensitivity to Noise and Initial Conditions

FIG. 17 shows the means and standard deviations of the fitted flow ratesfor two sets of simulated data (V_(art)=0.5%, F_(p)=60 ml/100 ml/min,V_(p)=3%; V_(art)=0.5%, F_(p)=20 ml/100 ml/min, V_(p)=2%), using themodel (FIG. 17 a) and SVD (FIG. 17 b) approach, respectively. Raw imagedata noise was varied from that of typical, clinical data (˜12) to 400.The SVD approach overestimates flow rates somewhat for this choice ofmodel parameters, whereas the vascular model fits are roughly equal tothe input parameters. The uncertainty (error bars in FIGS. 17 a and 17 bindicate one standard deviation, derived from the simulated data) onfitted flow rates display the expected increase as a function ofincreasing raw image data noise.

For low SNR, error bars are roughly equal in size for the SVD and modelapproach, respectively. For high SNR, however, the uncertainty onvascular model fits did not reach zero as was the case for the SVDapproach. To investigate whether factors other than noise contributed tothe observed behaviour, the dependence of model fits on initialconditions and the tendency of parameters to co-vary was analysed. Thefraction of fits, where initial conditions were found to significantlyaffect the fitted flow rates (defined as cases where two differentinitial conditions resulted in fitted flows that differed by more than10% from their mean) was found to be negligible for SNR above 20. Forlower SNR, 15–20% of fits gave ambiguous results. Therefore, thestandard deviations for the low SNR may be somewhat underestimated dueto bias by the choice of initial conditions. During simulations, fittedfeeding artery volumes and fitted tissue flows were found to co-vary:high, fitted flow rates were hence often accompanied by high arterialvolumes. FIG. 18 shows fitted flow rates versus corresponding fittedfeeding artery volumes from simulated curves with SNR=40. This patternof co-varying fitted flow rates and feeding artery volumes was found atall noise levels. It was found that varying flow and feeding arteryvolume in proportion lead to only small changes in the shape of theresulting concentration time curve. Therefore, the presence of modestexperimental noise leads to relatively large uncertainties in fittedflow rates. This is thought to explain the unexpected, large standarddeviation of flow estimates at high SNR for the vascular model, as wellas the fluctuations around unit relative flow in FIG. 16.

Discussion

Overall Validity of Model

The vascular model, after incorporation of the experimentally determinedheterogeneity PDF, provided excellent fits to the experimental data. Themodel fits of CBF yielded a mean gray:white flow ratio of 2 8±0.35, inagreement with the PET literature ratio of 2.65 for subjects of similarage (Leenders 1990). The ratios were also in good agreement with thosefound using the model-free approach. In contrast to the SVD approach,the model approach provided fits to experimental data that wereessentially independent of vascular delay. The model was simplifiedconsiderably by the use of one flow heterogeneity PDF for all types oftissue. By characterising the model by only three parameters, aremarkable stability of the model was obtained, even compared to thepixel-by-pixel based SVD approach. Co-varying vascular volume and flowrate in model fits to low SNR data was found to be a major contributorto uncertainty in model fits of CBF. Below, the individual elements ofthe model are discussed in further detail.

Model Considerations

The model presented here differs slightly from that previously describedby Kroll et al. (Kroll 1996) in the heart. Kroll et al. (Kroll 1996)described the arteriolar and capillary compartments separately,assigning fixed relative dispersion and variable volumes to thearteriolar vascular paths, and a fixed volume to the capillary bed. Inthe brain, capillary density varies greatly among different tissuetypes. For the purpose of obtaining a robust model for all types ofbrain tissue with the same choice of basic model parameters, themicrovascular volume was kept as a free parameter. In terms of vasculartransport, the models are similar, except that in the model presentedhere, dispersion takes place only in the large vessel, whereas smallvessel dispersion is accounted for by the flow heterogeneity PDF.Despite the simplification of the model, it is likely that, by limitingthe number of vascular elements and thereby the number of freeparameters, the stability of the model to noise has increasedsignificantly, as outlined in the analysis above. The robustness of themodel to experimental noise is imperative to ultimately study CBF athigh spatial resolution. Kroll et al. assumed that only small vesseltracer levels are observed by the residue detection (Kroll 1996). Here,this assumption is further justified by the inherent sensitivity ofsusceptibility contrast to microvessels (Fisel 1991; Weisskoff 1994;Boxerman 1995).

Vascular Transport and Dispersion Term

As discussed elsewhere (Østergaard 1996b), nonparametric deconvolutionapproaches do not allow separation of macrovascular transport andmicrovascular retention. Therefore, modelling vascular retention isnecessary, whenever vascular transport significantly changes the inputbolus shape upstream of the AIF measurement site. The vascular transportoperator model used in the present model is generally accepted formodelling normal major vessel transport. The advantage of includingvascular transport in the kinetic modelling is demonstrated in FIG. 14:The fact that tracer arrives earlier in tissue with high flow rate dueto a faster feeding vessel transit is accounted for by the modelapproach, unlike the model-free SVD approach. The difficulty inintroducing this operator lies mainly in the fact that the transferfunctions of the major vessel and the microvascular network are verysimilar. This, in turn, leads to the difficulty in separating vascularvolume and flow, as observed in the simulations (FIG. 18). The analysispresented here also suggest that this effect contributes significantlyto the uncertainty of flow estimates, even at modest noise levels, justat it may play a role in the dependency upon initial conditions offitted flow rates. These findings are in agreement with those previouslyreported by Kroll et al (Kroll 1996). In cerebrovascular diseases, bloodmay pass through stenoses with marked turbulence, or through irregularcollateral paths upstream of the arterial sampling site. In these cases,the vascular operator may not be adequate, and the vascular transportfunction should ideally be measured independently. Indeed, novel MRtechniques detecting the inflow of spin labelled arterial blood to agiven brain region may ultimately provide this information (Wong 1997).Such independent measurements would serve to avoid the interdependenceof flow and vascular volumes using vascular models, or alternativelyallow application of the model-free SVD approach. In severe cases,however, vascular dispersion may dominate total tracer retention, inwhich case estimates of flow rate by residue detection of anintravascular tracer become uncertain (Østergaard 1996b; Kroll 1996).

Flow Heterogeneity

Reports of cerebral flow heterogeneity are mainly based on invasivemeasurements of plasma or red blood cell velocities in rats. Abounaderet al. utilized bolus injection of a plasma marker followed bydecapitation, deriving plasma flow velocity from capillary filling inhistology (Abounader 1995). Hudetz et al determined the frequency of redblood cell (RBC) velocities in capillaries using intravital videomicroscopy (Hudetz 1997). Both found the distribution of blood elementsto be very heterogeneous, with a right-skewed shape. FIG. 19 shows theirfindings along with the PDF determined here. The data of Hudetz et al(Hudetz 1997) were normalised as the relative flow PDF (See Theory,Equation 9). From the data of Abounader et al. (Abounader 1995), anormo-capnic data set was chosen, and axes scaled to facilitatecomparison with the other curves (plasma flow units did not allow directnormalisation). It should be noticed that these measurements are notdirectly comparable. First, plasma and RBCs follow different pathsthrough the capillary network, so the measurements presented here shouldbe more comparable to the plasma velocity measurements. Secondly, theflow distribution curve derived in this study assumes equal capillarylengths. Although the relationship between capillary plasma flow andflow velocity is a complex function of capillary length andarchitecture, a finite distribution of capillary lengths is likely toresult in blood velocities being more dispersed than relative capillaryflows (As seen when comparing the PDF presented here with the RBCvelocity study). The similarity of the present measurements with theseindependent, invasive methods lends hope to the use of this approach indescribing normal microvascular dynamics. In altered physiologicalstates or disease, the flow heterogeneity may not be as constant amongtissue types as found in this study. Abounader et al. (Abounader 1995)determined the heterogeneity of microvascular flow at different degreesof hypercapnia, and found that plasma flow became more homogenous athigher flows. A similar finding for red blood cell velocities wasreported by Hudetz et al (Hudetz 1997). This could be the case indisease as well, and caution should therefore be exercised in choosingflow heterogeneity PDF for use with vascular models in these cases. Themodel-free approach to determine flow heterogeneity PDF presented heremay provide insight with respect to the distribution of relative flowsin these cases. Using this approach, it should be kept in mind solvingEquation 1 belongs to a class of so-called inverse problem, meaning thatany noise in measured tissue concentrations may lead to large changes inthe resulting residue function. As suppression of noise inevitablycauses loss of underlying information, the SVD deconvolution thereforemay not yield the exact shape of the underlying residue function.Likewise, one may not be able to distinguish slightly different flowheterogeneity PDF based on noisy measured concentration time curves.Although the flow heterogeneity PDF and derived flow rates were found inagreement with independent findings, it is therefore important tofurther validate the approach presented here.

Utility of Vascular Models

Although cerebral blood flow itself is an important index of brainfunction, the heterogeneity of microvascular flow and transit timesdescribed here may be a more important determinant of cerebralmetabolism. As discussed by Kuschinsky et al., the degree ofheterogeneity among capillary paths determines the netcapillary-to-tissue concentration gradients necessary to drive deliveryof nutrients (Kuschinsky et al., 1992). Indeed, regulation of capillaryflow heterogeneity may play a major role in the brains ability toincrease e.g. oxygen delivery to meet cellular metabolic demands(Kuschinsky et al., 1992). This issue can be addresses in great detailby combining flow heterogeneity measurements with spatially distributedmodels of oxygen exchange (Li 1997). The analysis presented here,combined with these models, may ultimately lead to a more extensiveunderstanding of, for example, the fundamental limitations of oxygendelivery in stroke, where the survival of tissue may partially depend onthe ability to increase oxygen extraction by an increased mean transittime. Also, modelling the exact relationship between cellular oxygenconsumption and vascular oxygen levels may facilitate a quantitativemetabolic interpretation of deoxyhemoglobin concentration changesobserved by functional magnetic resonance imaging (Kwong 1992).

EXAMPLE 4

Magnetic Resonance Imaging Measurements of Flow HeterogeneityDemonstrate High Risk of Infarction in Acute Stroke

Summary of the Example

The ability of brain tissue to survive ischemic episodes is believed tobe related to changes in the dynamics of capillary blood flow. Using anovel magnetic resonance imaging based method to measure microvasculartransit time dynamics, the flow heterogeneity and tissue mean plasmatransit times was examined in 11 patients presenting with acute (<12hours after symptom onset) stroke. In normal brain tissue, thedistribution of relative flows was found to be markedly skewed towardshigh capillary flow velocities. Within regions of decreased cerebralblood flow, plasma mean transit times were prolonged. Furthermore,subregions were identified with significant loss of the high-flowcomponent of the flow distribution, thereby causing increasedhomogeneity of flow velocities. These findings are in agreement withindependent, invasive measurements of flow heterogeneity in states ofdecreased perfusion pressure in animal models. In parametric mapsquantifying the acute deviation of flow heterogeneity from that ofnormal tissue, areas of extreme homogenisation of capillary flowspredicted final infarct size on follow-up scans in 10 out of 11patients. Flow heterogeneity and plasma mean transit time can be rapidlyassessed as part of a routine clinical magnetic resonance examination,and may provide a tool for individual planning of stroke treatment, aswell as in targeting and evaluating emerging therapeutic strategies.

Background

Acute stroke is the third leading cause of death, and the leading causeof adult disability. Emerging therapeutic strategies seek to minimisethe progression of tissue damage in the acute phase of the disease.Methods to rapidly assess the severity and later progression of acutestroke in individual patients are therefore highly desirable to planindividual treatment, as well as to evaluate novel therapeuticstrategies.

In acute cerebral ischemia, delivery of nutrients is severelycompromised, and tissue survival therefore depends on tissue regulatorymechanisms to meet metabolic needs. Studies using positron emissiontomography (PET) have shown that mean blood transit time (MTT) and, withfurther drop in cerebral perfusion pressure, also the oxygen extractionfraction (OEF) are increased in ‘tissue at risk’ of infarction (Gibbs1984; Baron 1981). Although the relationship between prolonged blood MTTand OEF remains unclear, both phenomena are believed to reflectunderlying regulatory mechanisms attempting to compensate for a decreasein perfusion pressure.

One mechanism for vasoregulatory control is believed to be the abilityto alter the heterogeneity of blood transit times and thereby the meancapillary concentration of substances diffusing from blood to tissue(Kuschinsky and Paulson 1992). Animal experiments in rats have revealeddecreased flow heterogeneity during whisker-barrel stimulation (Vogeland Kuschinsky 1996), indicating that this may be the mechanismunderlying the normal brain's striking ability to meet increasedmetabolic needs during functional activation. Furthermore, Hudetz et al.demonstrated that graded decrease in perfusion pressure causesprogressive loss of high-flow components, thereby decreasing total flowheterogeneity (Hudetz 1996). Decreasing-flow heterogeneity thereforeseems to play a crucial role in maintaining sufficient concentrationgradients to drive diffusion of nutrients such as oxygen from blood intothe cells (Kuschinsky and Paulson 1992). This suggests that blood meantransit time and the degree of flow heterogeneity are important indicesto assess and further understand the ability of the brain to surviveischemic episodes.

The heterogeneity of flows in normal volunteers by magnetic resonanceimaging (MRI) residue detection has recently been studied (Example 3(Østergaard 1999)). It was found that the probability density function(PDF) of relative flows was remarkably constant within and among normalvolunteers. In this study, magnetic resonance residue detection was usedto study plasma mean transit times as well as flow heterogeneitypatterns in patients presenting with acute stroke. Furthermore, thesefindings were correlated with later neuronal death by comparing initialdiffusion weighted imaging (DWI) with follow-up MRI or computedtomography (CT).

The present findings show that flow heterogeneity changes, previouslyonly detectable by invasive microscopy in animal models, can be assessedby a 2-minute examination as part of routine MRI of acute strokepatients. Furthermore, the degree of heterogeneity change relative tonormal tissue is a powerful predictor of later neuronal death,suggesting flow heterogeneity may provide an important diagnostic toolin stroke patient management.

Materials and Methods

Patient Data

All patients were treated with best medical management, but did notreceive tPA or other thrombolytic traeatment. DWI and CBF results forthese patients are reported earlier (Sorensen 1998).

Imaging was performed on a GE Signa 1.5 T imager (General Electric,Waukesha, Wis.) retrofitted for EPI capabilities (Instascan, AdvancedNMR Systems, Wilmington, Mass.).

MRI Perfusion Protocol. Determination of CBV, CBF, MTT, and flowheterogeneity. Perfusion imaging was performed using spin echo (SE) orgradient echo (GE), echo planar imaging (EPI) with a time of repetition(TR) of 1.5 seconds, and a time of echo (TE) of 100 ms (50 ms for GEEPI). The slice thickness was 5 mm with an in-plane resolution of 1.56mm by 1.56 mm in a 40 by 20 cm field-of-view (FOV). In 10 slices, atotal of 52 images were acquired, starting 15 seconds before i.v.injection of 0.2 (SE-EPI) or 0.1 (GE-EPI) mmol/kg Gd-based contrastagent. Intravascular contrast agent concentrations, C(t), werequantified assuming a linear relationship between concentration andchange in transverse relaxation rate, ΔR₂ (Villringer 1988; Weisskoff1994). The shape of the arterial input function (AIF) was determinedfrom feeding arterial branches either adjacent to the area of DWIabnormality or at the contralateral middle cerebral artery (MCA), andwere, identified in the image slice as pixels displaying earlyconcentration increase after contrast injection (Porkka 1991). Thetissue residue function (or impulse response function) was calculated bydeconvolving the tissue concentration time curve by the AIF, usingsingular value decomposition (SVD) (Østergaard 1996a; Østergaard 1996b).CBF was determined as the height of the deconvolved tissue curve. CBVwas determined by the area under the tissue concentration time curve, aspreviously described (Rosen 1990), and the plasma mean transit time(MTT) formed as the ratio CBV/CBF (Stewart 1894). Finally, thedistribution of tissue transit times in each imaging voxel wasdetermined as the slope of the residue function, and by assuming equallengths of capillary paths, the corresponding probability densityfunction (PDF) of relative flows was determined by means of the centralvolume theorem (Stewart 1894; Example 3 (Østergaard 1999)). In order toquantify and compare the deviation of the experimentally determined PDFfrom that found in normal brain, a Kolmogorov-Smirnov test wasperformed, comparing the flow PDF in a given pixel to that previouslydetermined in normal tissue (See Results, FIGS. 20 a, 20 b and 20 c)(Press 1992; Example 3 (Østergaard 1999)). The corresponding p-value(Null-hypothesis: flow heterogeneity distribution is equal to that ofnormal tissue) was considered statistically significant if p<0.01(Without Bonferoni correction).

Initial and Final Infarct Sizes.

At the initial scan, infarct size was assessed by diffusion weightedimaging (DWI) (Moseley 1990), acquired using single-shot EPI (TR 6 s, TE118 ms) with diffusion weighting applied in 6 directions. By combininglow (b=3 s/mm²) and high b-values (ranging from 892–1221 s/mm²), theentire diffusion tensor was sampled. Measurements were performed in17–20 6 mm thick slices with 1 mm interslice gap, with an in-planeresolution of 1.56 mm to cover the whole brain. The resulting isotropic(tensor trace) diffusion weighted image was used in assessing initialinfarct size. Final infarct size was assessed from DWI images acquired2–5 days after the infarct, from T₂ or FLAIR MR images acquired at least5 days after the infarct, or from CT images acquired more than 5 daysafter the infarct if no MRI was available.

Volumetric Analysis

Using a semi-automatic image analysis software package (ALICE, HaydenImage Processing Group, Boulder, Colo.), volumes of decreased diffusion,prolonged MTT and abnormal p (p<0.01), respectively were measured bymanually drawing regions of interest (ROI) around the lesions on thecorresponding maps, multiplying the lesion areas by the slice thicknessplus inter-slice gap. We did not attempt to co-register initial andfollow-up studies.

Results

Eleven hyperacute stroke patients, 7 male and 4 female, with mean age 61(range 33–80) years, were examined within 12 hours of symptom onset(Table 6). All patients showed diffusion abnormalities on the initialDWI (Moseley 1990), consistent with ischemic neuronal death prior to theinitial scan. Furthermore, all patients showed greater volumes ofdecreased cerebral blood flow (CBF) and/or increased MTT in thehemisphere of infarction.

TABLE 6 Patient Age/sex Hours 1 33 M 4.5 2 78 F 3 3 55 M 2 4 53 M 3 5 72F 2.5 6 64 F 5.5 7 79 M 7.0 8 80 F 11.0 9 45 M 4.0 10 65 M 11.5 11 45 M6.5Age, sex, time of initial MRI for 11 acute stroke patients. Patient 9showed spontaneous reperfusion of the occluded vessel on the follow-upMR angiography.Flow Heterogeneity Findings

Outside volumes of prolonged MTT, the shape of the tissue flow PDF wassimilar to that previously found in normal volunteers, namely aright-skewed distribution with a distinct distribution of high flowrates. Inside volumes of prolonged mean transit times, the shape of theflow PDF was either like that of normal tissue, or showed distinctiveloss of the high-flow portion of the PDF. To illustrate the first type,FIGS. 20 a, 20 b, and 20 c show a typical pattern in patient 6. Thispatient, a 64 year old female, was examined 5.5 hours after onset ofleft leg weakness, and showed prolonged MTT corresponding to theanterior cerebral artery territory (FIG. 20 a). FIG. 20 b shows the flowheterogeneity plots for normal brain tissue as well as two regions ofprolonged mean transit time (Areas are indicated on the MTT map withnumbers corresponding to the PDF curves). The flow PDF in normal tissuewas markedly right-skewed, and matched the shape previously found innormal volunteers (Example 3 (Østergaard 1999)). The volumes ofincreased MTT displayed PDFs with a more symmetric shape, with atendency to loose the high-flow population found in normal tissue. Thedegree of symmetry varied within the volume of increased MTT. Thedeviation from the normal PDF was subsequently quantified by aKolmogorov-Smirnov test, yielding the probability p that the curvebelong to the distribution of relative flows of normal tissue (fromExample 3 (Østergaard 1999)). In FIG. 20 c, areas with large deviationsof the PDF from that of normal tissue (p<0.01) are shown by a colourcoded overlay of p onto the acute CBF map. Based on the previousexperience (Example 3 (Østergaard 1999)) a significance level of p<0.05displays few PDF abnormalities in normal tissue, except in majorvessels. Therefore, p<0.01 was chosen to highlight highly significantdeviations from normal flow heterogeneity PDF.

MTT, Flow Heterogeneity and Later Infarction

In 8 out of 11 patients, comparison of initial DWI images with thefollow-up study showed that lesion size had increased in between theinitial and follow-up scans. In all 8 cases, neuronal death had occurredwithin the region initially displaying increased MTT. FIGS. 21 a and 21b show this correlation in patient 11, a 45-year-old male 6.5 hoursafter onset of symptoms. On the initial DWI (first row), cell death islocalised to deep gray matter, whereas the acute MTT maps (second row)show prolonged MTT corresponding to the whole middle cerebral arteryterritory. The p-map shows highly significant deviations from the normalflow PDF in anterior and posterior sub-regions. These subregionscorresponded well with tissue that later infarcted, displayed as brightregions in the 2-month follow-up FLAIR MRI images (bottom row). In FIG.22, final infarct volumes are compared to the initial abnormalities ofDWI+MTT and DWI+p maps, respectively. Notice the striking ability ofcombined initial DWI and p-maps to predict final infarct size. In 10 outof 11 patients, p maps (excluding vessels and volumes with preserved,high flow component, see below) corresponded well with the finalinfarct. FIGS. 23 a and 23 b show the respective maps from patient 3.Notice that the initial lesion (top row) and extent of MTT prolongation(second row) are similar to that observed in FIGS. 21 a and 21 b.Although the CBF was significantly decreased (Third row, gray scaleimage), there were only small abnormalities in the flow heterogeneities(indicated by coloured areas on overlay on the CBF map). The small spotscorrespond to vessels, having a high degree of flow heterogeneity. Thefinal infarct size was similar to that observed on the initial DWI,indicating that the heterogeneity may again have served as a predictorof final outcome.

To demonstrate the predictive value of the p-maps in cases of whitematter ischemia, FIGS. 24 a and 24 b show maps from patient 9, a 80 yearold female. Small infarcted areas are seen on the initial DWI images(Top row). The MTT image shows abnormalities extending into white matteraround the initial lesions. Again, flow heterogeneity changes areobserved in smaller subregions, corresponding well to the regions thatwent on to infarction. Notice symmetrically located areas with low pvalues, corresponding to vessels.

Artifacts in p-Maps

In one case, (patient 9), p maps underestimated the final infarct size.FIG. 25 shows one slice from this patient, displaying areas with p<0.1.Notice high-intensity areas correspond to areas that later infarcted,whereas a number of areas showed unspecific p increase. Separateevaluation of areas with p<0.01 would in this patient causeunderestimation of final infarct size. Interestingly, follow-up MRangiography in this patient demonstrated spontaneous reperfusion betweeninitial and follow-up scans. In the p-maps, small areas of low p-valueswere in some cases observed at the location of major vessels (See FIGS.21 b and 24 b), due to the homogenous flow pattern in vessels relativeto that in tissue. These areas were not included when defining areas ofabnormal tissue flow heterogeneity for comparison with follow-upstudies. In patients 3 and 4, areas unrelated to major vessels showedlow p-values in a single slice, whereas adjacent tissue in neighbouringslices showed no abnormalities. Analysis of the flow heterogeneity PDFin these single slices revealed a high-flow distribution similar to thatof normal tissue, whereas the low-flow component showed flow componentsdown to zero (unlike the relatively sharp cut-off at 0.5 observed innormal tissue—See FIG. 20 b). This is interpreted as being due todispersion of the AIF relative to the tissue. Based on the preservedhigh-flow component and the normal PDF observed in adjacent tissue inneighbouring slices, these areas were not included when comparing p-mapswith follow-up images. Below these phenomena are further discussed.

Discussion

The study confirms the report by Hudetz et al in animals that decreasedperfusion pressure (CBF:CBV ratio) is associated with progressive lossof high-flow components (Hudetz 1996). The study extends these findingsby documenting loss of flow heterogeneity in human acute stroke, andgood agreement between heterogeneity changes in early ischemia andeventual tissue infarction. The findings presented hence stronglysupport the hypothesis by Hudetz et al that gradual loss of the highflow component of the flow heterogeneity PDF heralds local loss offunctional reserve capacity, and thereby neuronal death (Hudetz 1996).The finding that p-maps predict final infarct size with high certaintyin untreated patients suggest that MR heterogeneity measurements mayprove useful for individual planning of patient management, as well asfor evaluation of new therapeutic approaches in smaller patientpopulations.

The hypothesis of heterogeneity changes being the driving force inregulating oxygen delivery to tissue (Kuschinsky and Paulson 1992; Vogeland Kuschinsky 1996) suggest a close relationship between the findingspresented here and the OEF increase observed by PET in tissue at highrisk of subsequent infarction (Powers 1991; Wise 1983). Indeed,qualitative analysis of the kinetics of oxygen delivery show that oneshould expect reduced heterogeneity of blood flow to produce anincreased flow of oxygen into the tissue in states of decreased flow, asillustrated in FIG. 26. The curve is a plot of the oxygen flow intotissue versus blood flow. From the convex shape of the curve it can beseen that oxygen flow into the tissue at a given mean blood flow isgreater when blood flow is homogenous than when blood flow is moreheterogeneous: Oxygen flow into tissue versus blood flow F_(t), relatedthrough the equation F_(t)·(1−e^(−PS/F) _(t)), where PS is thepermeability to oxygen times the surface area of capillaries (Renkin1959; Crone 1963). If all blood flow is at the normal mean flow,f_(norm), the oxygen flow into tissue is given by the height of A. Ifpart of the flow is at f_(low) and the rest at f_(high), with weightingsto maintain the same mean flow, the oxygen flow into the tissue will bethe height of D. Notice, as mean flow is reduced and f_(high) andf_(low) changed to maintain the same CMRO₂, both f_(low) and f_(high)approach f_(min), thereby decreasing the degree of heterogeneity. Noticedecreased flow heterogeneity with constant flow will increase oxygendelivery, in parallel with the findings of Vogel et al, who founddecreased heterogeneity in states of functional activation and therebyincreased oxygen metabolism (Vogel and Kuschinsky 1996).

The observed shifts toward a homogenous flow distribution may thereforesignal increased utilisation of metabolic regulatory capacity,explaining the risk of neuronal death observed in these regions ofextreme flow homogenisation. PET is today the method of choice todemonstrate metabolic reserve capacity in cerebrovascular disease.However, future studies should focus on the relationship between MR flowheterogeneity measurements and OEF measured by PET to further explorethis coupling of microvascular dynamics and metabolism.

Neuronal death was localised in areas initially displaying prolongedplasma mean-transit times. This is agreement with the previousexperience using this technique (Sorensen 1998), as well as studiesusing PET (Heiss 1994; Baron 1981) and single photon emission computedtomography (SPECT) (Buell 1988). Although the CBV:CBF ratio (i.e. 1/MTT)depends linearity on the cerebral perfusion pressure over a range ofvalues (Schumann 1998), this dependence is likely to be lost whenmaximum vasodilation is reached at low pressures (Powers 1991). The MTTprolongation may therefore not be directly related to the severity ofthe perfusion pressure drop and hence risk of infarction. The findingssupport, however, that prolonged MTT is an early sign of decreasedperfusion pressure, at a stage where regulatory mechanisms may stillsuffice to ensure tissue survival.

Although the high flow component seem crucial to tissue survival, thelow flow component of the flow heterogeneity PDF may also prove usefulin planning therapeutic approaches. Intravital microscopy studiessuggest that maintaining capillary flow velocities above a fixed, lowerlimit is essential to avoid white blood cell plugging of capillaries(Hudetz 1996; Yamakawa 1987). The distributions of absolute flows insingle pixels may prove useful in assessing of leukocyte adhesion priorto therapeutic attempts to reperfuse tissue.

In patients with cerebrovascular disease, the AIF may undergo dispersionand delays upstream of site of measurement, possibly causingoverestimation of MTT (Østergaard 1996a; Østergaard 1996b). This biaswas reduced by choosing AIFs in the vascular territory affected by thevascular occlusion. Furthermore, dispersion of the AIF will tend tobroaden the flow PDF. Therefore, the effects of dispersion counteractthe observed homogenisation of flow elements. In determining the flowPDF, high p values were observed near vessels (and therefore easilyidentifiable on the accompanying CBV maps), as major vessel flowinherently homogenous. Probability maps should therefore be carefullyinspected for vessels on CBV maps, as well as signs of vessel dispersionin the PDF shape in a given region. SE-EPI images are particularlysuited for this type of analysis, as large vessels are suppressed due tothe inherent microvascular weighting of these images (Fisel 1991;Boxerman 1995; Weisskoff 1994).

Given these precautions, the findings presented here indicate thatmagnetic resonance based assessment of flow heterogeneity provides apowerful tool to study residual metabolic reserve capacity inperi-infarct tissue. Combined conventional MRI, MR angiography, DWI,determination of flow heterogeneity and plasma mean transit time can beperformed in roughly 20 minutes on most clinical MR systems. Unlike PETand SPECT, examinations can therefore be performed within the shorttime-window where treatment should be initiated in order to prevent theprogression of neuronal death. Presence of tissue with loss of flowheterogeneity may in the future serve to guide individual patientmanagement, and point to tissue that may serve as target for noveltherapeutic approaches

EXAMPLE 5

Renal Plasma Flow, Volume and Transit Time Heterogeneity Measured ByMagnetic Resonance Imaging

Introduction

Noninvasive methods for assessing individual renal function areessential in diagnosis of disease as well as in subsequent monitoring ofdisease progression, especially the deterioration of renal function inrenal artery stenosis, diabetes, ureteral obstruction, neurogenicbladder, and to identify rejection or other postoperative complicationsin renal transplants. The questions often asked is whether function isstable or deteriorating, thereby detecting changes at early stages wheretreatment may still be possible, or in some cases in unilateral diseaseto determine whether the patient may benefit from nephrectomy.

Existing Techniques for Assessing Renal Function

Unilateral renal function is today almost exclusively determined byradionucleide measurements, using mostly ^(99m)Tc, ⁵¹Cr or ¹³¹I/¹²³Ibound agents and gamma camera detection. The radiotracers fall intothree main groups, filtered agents that are exclusively filtered in theglomeruli, secreted agents that are totally removed from the blood intothe urine during a single transit, and finally the more rare boundagents which display some degree of binding to the renal parenchyma.

Filtered agents (mainly ^(99m)Tc-DTPA) are filtered in the glomeruli andthereby give a direct measurement of glomerular filtration rate (GFR).As only a fraction of the total plasma flow to the kidney is filtered(roughly 20%), use of these agents give no direct information on renalblood flow.

Secreted agents (e.g. ^(99m)Tc-MAG₃, ¹²³I/¹³¹I-OIH) are almost totallyremoved (˜90%) from the blood during a single transit, and the rate atwhich it disappears from the blood and appears in the urine is thereforeproportional to renal plasma flow (RPF).

Bound agents (e.g. ^(99m)Tc-DMSA, ^(99m)Tc-GHA) often show some extentof plasma binding as well as secretion into the urine. Ideally, however,these agents would show regional uptake in the parenchyma proportionalto tissue flow.

Functional Parameters

The functional indices derivable from dynamic images acquired afterinjection of these agents are closely related to the characteristictransport and uptake over time. The early phase (˜1 minute) after theinjection of either filtered or secreted agent mainly display theinitial, vascular distribution of the tracer and is referred to as thevascular transit segment. This phase is to some extent related to renalblood flow, as a rapid transit presumably signal high blood flow.

The nephron transit segment (˜1–5 minutes, i.e. uptake/transport throughthe nepron) reflects GFR for a filtrated agent and RPF for a secretedagent.

The body transit segment (10–30 minutes) detects either clearance oftracer from the whole body or the appearance of tracer in the bladder.Again, by the properties of the tracer, the rate of clearance reflectsRPF for secreted agents and GFR for filtered agents

The role of macroscopic and microscopic haemodynamic changes in diseaseEvidence suggests that along with the gradual deterioration of renalparenchyma in acute and chronic renal disease, marked changes in overallrenal perfusion as well as renal microcirculation occur. These latterchanges range from abnormal tone in afferent arterioles (e.g.hypertension (Iversen 1998) and acute renal failure (Bock 1997)) leadingto abnormal pressure gradients and possibly loss of autoregulation(Iversen 1998), changes in the width and shape of glomerular capillariesin early stages of glomerular sclerosis (Nagata 1992) and finallyextreme heterogeneity of transit time in the peritubular capillaries inexperimental uremia (Shea 1984).

These states of abnormal pressure or vascular structure all lead tochanges in plasma transit time characteristics (pressure gradientschange transit time as this is roughly the inverse of the perfusionpressure) at a regional, glomerular or even post-glomerular capillary(Shea 1984) level. Although regional flood flow and transit timedynamics may be important in early detection of pathological changes inrenal disease, the ability to characterize microscopic changes intransit time distributions may therefore enhance the ability to detectearly changes in disease development.

Possible Future Role of Magnetic Resonance Imaging (MRI)

Contrast enhanced MR imaging using Gd-chelates such as Gd-DTPA provide acomplete analogue to ^(99m)Tc-DTPA renography for GFR measurements, butoffering superior spatial resolution and the advantage of being free ofexposure to ionizing radiation. With the development of purelyintravascular contrast agent, and techniques to assess plasma flow andplasma volume from residue detection techniques (Østergaard 1996), theseGFR measurements can be supplemented by high resolution haemodynamicinformation. Furthermore, novel developments in characterizingmicroscopic flow- and transit time heterogeneity (Østergaard 1999, Ex 1)may allow addressing the regional microscopic haemodynamics, therebypossibly improving diagnostic power of non-invasive tomographictechniques.

Aim of this Study

In this report, we used a recently developed method to determineregional plasma flow in the kidney after acute obstruction of oneureter. Furthermore, we applied a novel method to assess transit timedistribution in single pixels, in order to demonstrate the feasibilityof monitoring transit time characteristics on pixel-by-pixel level inthe kidney.

Materials and Methods

Animal Preparation and Experimental Protocol

Country-bred Yorkshire pigs weighing 30 kg were used in the experimentsPigs were initially sedated by i.m. injection of 0.25 ml/kg of a mixtureof midazolam (2.5 mg/ml) and ketamine HCl (25 mg/ml). A catheter wasthen placed in an ear vein. After i.v. injection of additionalmidazolam/ketamine mixture (0.25 ml/kg), the pig was intubated andartificially ventilated throughout the experiment, maintaininganesthesia by continuous infusion of 0.5 ml/kg/hr of themidazolam/ketamine mixture and 0.1 mg/kg/hr pancuronium. Indwellingfemoral arterial and venous catheters were surgically installed.Unilateral ureteral obstruction (UO) was induced by ligation of oneureter through a low midline incision.

MRI Protocol

Images were acquired on Gyroscan NT 1.5 Tesla whole-body system (PhilipsMedical Systems, The Netherlands) running the NT5 3. software version atUppsala University Hospital, Sweden.

Dynamic images were acqired using a Fast Field Echo (FFE) with arepetition time (TR) of 11.3 ms, echo time (TE) 8.0 ms and a flip angleof 12° Dynamic images could hence be acquired once every 1.2 second.Image Field Of View (FOV) was 280 by 280 mm with a 256 by 256resolution, leading to an in-plane resolution of 1.09 mm 1.09 mm at a 6mm slice thickness. A series of 60 dynamic images were acquired duringthe rapid bolus injection of 1 mg Fe/kg of NC100150, an ultra small ironoxide particle (USPIO) intravascular contrast agent (Nycomed-Amersham,Oslo, Norway).

Experimental data are courtesy of Lars Johannson and Atle Bjørnerud,Nycomed Imaging AS.

Renal Blood Flow and Transit Time Characteristics

We utilised the fact that the tissue impulse response to a plasma tracercan be estimated by non-parametric deconvolution of the tissue residueduring the tracer passage by a non-invasively determined AIF. From thiswe derive the distribution of plasma transit times. The tissueconcentration Ct(t) of tracer in response to an arterial input functionC_(a)(t) is given by

$\begin{matrix}{{C_{t}(t)} = {{F \cdot {{C_{a}(t)} \otimes {R(t)}}} \equiv {F \cdot {\int_{0}^{t}{{C_{a}(\tau)}{R\left( {t - \tau} \right)}{\mathbb{d}\tau}}}}}} & {{Eq}.\mspace{14mu} 24}\end{matrix}$where F is tissue flow and R is the residue function, i.e. the fractionof tracer present in the vasculature at time t after a perfect,infinitely sharp input in the feeding vessel. Assuming the arterial andtissue concentrations are measured at equally spaced time-points t₁, t₂,. . . , t_(N), this equation can be discretised, assuming that overshort time intervals Δt, the residue function and arterial input valuesare constant in time:

$\begin{matrix}{{C_{t}\left( t_{j} \right)} = {{F \cdot {\int_{0}^{t_{j}}{{C_{a}(\tau)}{R\left( {t - \tau} \right)}{\mathbb{d}\tau}}}} \approx {\Delta\;{t \cdot F \cdot {\sum\limits_{i = 0}^{l}{{C_{a}\left( t_{i} \right)}{R\left( {t_{j} - t_{i}} \right)}}}}}}} & {{Eq}.\mspace{14mu} 25}\end{matrix}$or

$\begin{matrix}{{{F_{t} \cdot \Delta}\;{t \cdot \begin{pmatrix}{C_{a}\left( t_{1} \right)} & 0 & \ldots & 0 \\{C_{a}\left( t_{2} \right)} & {C_{a}\left( t_{1} \right)} & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots \\{C_{a}\left( t_{N} \right)} & {C_{a}\left( t_{N - 1} \right)} & \ldots & {C_{a}\left( t_{1} \right)}\end{pmatrix} \cdot \begin{pmatrix}{R\left( t_{1} \right)} \\{R\left( t_{2} \right)} \\\ldots \\{R\left( t_{N} \right)}\end{pmatrix}}} = \begin{pmatrix}{C_{br}\left( t_{1} \right)} \\{C_{br}\left( t_{2} \right)} \\\ldots \\{C_{br}\left( t_{N} \right)}\end{pmatrix}} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

As previously described (Østergaard 1996), this equation can be modifiedto residue and arterial input functions varying linearly in time, andsolved by Singular Value Decomposition (SVD) to yield the residuefunction. The distribution of transit times, h(t), is then found from

$\begin{matrix}{\left. {{R(t)} \equiv \left\lbrack {1 - {\int_{0}^{t}{{h(\tau)}{\mathbb{d}\tau}}}} \right\rbrack}\Rightarrow{h(t)} \right. = {- \frac{\mathbb{d}R}{\mathbb{d}t}}} & {{Eq}.\mspace{14mu} 27}\end{matrix}$i.e. the slope of the residue function. We therefore determined h(t) ata given time point t₁ as

$\begin{matrix}{{h\left( t_{i} \right)} = {{\frac{1}{2} \cdot \left( {\left( \frac{{R\left( t_{i} \right)} - {R\left( t_{i - 1} \right)}}{\Delta\; t} \right) + \left( \frac{{R\left( t_{i + 1} \right)} - {R\left( t_{i} \right)}}{\Delta\; t} \right)} \right)} = {\frac{1}{2} \cdot \left( \frac{{R\left( t_{i + 1} \right)} - {R\left( t_{i - 1} \right)}}{\Delta\; t} \right)}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$

In order to make measured transport functions comparable, they werenormalised to the mean transit time by requiring∫₀ ^(∞) τ·h(τ)dτ=∫ ₀ ^(∞) h(τ)dτ=1  Eq. 29Tissue and Arterial Concentration Estimates

Tissue concentrations were estimated assuming the concentration at timet, C_(t)(t), is proportional to the change in transverse relaxationrate, i.e.

$\begin{matrix}{{C_{t}(t)} = {{- k} \cdot {{\log\left( \frac{S(t)}{S\left( t_{0} \right)} \right)}/{TE}}}} & {{Eq}.\mspace{14mu} 30}\end{matrix}$where S(t₀) is the baseline signal intesity, S(t) the signal intensityat time t and TE the echo time (k is here a constant depending on thecontrast agent and the blood characteristics). Arterial concentrationswere obtained in a similar manner, from pixels located at the renalartery in the hilus region.Results

FIG. 27 shows typical parametric renal flow images acquired, immediatelyafter and 105 minutes after ureteral occlusion. Note the high spatialresolution (1.09 by 1.09 mm) compared to the roughly 10 by 10 mmresolution of most radionucleide scans. Also note high contrast oversurrounding muscle tissue displaying much lower plasma flow. Generally,little problems due to motion during the dynamic imaging session wasexperienced. In FIG. 27 is shown images showing high resolution imagesof relative renal plasma flow 15 minutes after (left) and 105 minutesafter (right) obstruction of the left ureter (located at right hand sidein the images). Notice the dilation of the left kidney and markedreduction in flow after obstruction

FIG. 28 shows the temporal evolution of renal plasma flow and volumeafter ureteral occlusion. Notice the gradual and parallel decrease inboth quantities after occlusion, reaching 20% after 100 minutes. Theplasma volume displays a short increase immediately after occlusion,seemingly keeping plasma flow at constant values. In FIG. 28 is showntemporal evolution of renal plasma flow and volume after ureteralocclusion. Whole kidney parenchyma was manually segmented by an imageanalysis program (Cheshire, Hayden, Boulder, Colo.). For the normalkidney, a similar Region Of Interest could be used for all time points,but for the occluded side, ROI's had to be adjusted to take dilationinto account. The occluded kidney values were then normalized to thecontralateral side. Notice the gradual and parallel decrease in bothquantities after occlusion, reaching 20% after 100 minutes. The plasmavolume displays a short increase immediately after occlusion, seeminglykeeping plasma flow at constant values.

FIG. 29 shows transit time characteristics measured as the averagedtransport functions in 4 pixels from to regions. In most of the renalparenchyma, normalized transport functions were of similar shape. Onlythe tissue at the base of the pyramids showed a slightly more homogenoustransit time distribution. Transit times were of the order of 1 second,and relatively uniform across the kidneys. No differences betweenkidneys were observed in the transit time distributions in ureteralobstruction. In FIG. 29 is shown distribution of transit times relativeto the mean transit time. The shape of the distribution was veryhomogenous across the paranchyma (full line): One exception was noticedin the pyramids (Dashed line) with a slightly more homogenousdistribution of transit times. We speculate this may be due to afraction of the vessels being vasa recta in this ROI. These ROIs maydisplay a more homogenous flow distribution due to the difference incapillary organization in pyramids relative to cortical areas.

Discussion

Our results showed marked, acute decrease in RPF and RPV immediatelyafter obstrution of the ureter. The plasma flow reduction was 20% withinthe first hour after occlusion. The change is somewhat smaller than the35% decrease observed by Frøkjær et al. (1996) by electromagnetic flowprobes directly in the renal artery, and 33% by Claudon et al. usingDoppler ultrasound (Claudon). This difference may owe to methodologicaldifferences between arterial flow velocity measurements and tomographic,tissue level flow measurements. The parallel reduction in RPV indicatesthat the obstruction is associated with a vasoconstriction, in agreementwith previous findings (Frøkjær 1996). Our findings suggest a transientincrease in blood transit time after obstruction (the volume:flow ratioand thereby the transit time increase is seen in FIG. 28), indicatingdecreased perfusion pressure (The inverse of the transit time).Perfusion pressure was normalized, however, after roughly 30 minutes.

The distribution of transit times could be recorded on a pixel-by-pixelbasis, suggesting that microvascular haemodynamic changes can indeed bestudied, thereby characterizing microscopic changes in disease. Asmentioned in the introduction, transit time are closely associated withthe changes in nepron vascular ultrastructur, and high resolutiontransit time characteristics may therefore at some point aid in theearly detection of disease. No asymmetries in transit time distributionswere detected in this acute occlusion study, in agreement with the factthat microcirculation is believed to remain intact in acute phases ofacute occlusion.

The use of MRI offers the advantage of high resolution images of notonly blood flow and volume, but also the possibility of high resolutionstructural MR images, magnetic resonance angiography and—with theaddition of a small Gd-chelate contrast agent—high resolution GFRimages. Imaging can be performed without subjecting the patient toionizing radiation, and with only limited time consumption beyond atraditional radionucleide renography.

We observed tissue mean transit times of the order of 1 second in thisstudy, suggesting high image sampling rate is essential, just thearterial input reaching the tissue must be very sharp to accuratelydefine tissue transit time characteristics. It is believed, however,that this will be within reach in a clinical setting with currentmethods and technology. Also, we believe that water relaxationcharacteristics in the kidneys may need further study with the contrastagent used. Fist, T₁ relaxation effects may become important, just as wespeculate that the 80% reduction in glomerular filtration rate (GFR)also observed in acute obstruction (Hvistendahl 1996) may disturb normalwater exchange between capillaries and tubuli, thereby affectingmeasurements slightly.

EXAMPLE 6

Flow Heterogeneity of Cerebral Neoplasms—a Measurement of MicrovascularTortuosity?

Tumor growth is limited by the neoplasms ability to stimulatesurrounding tissue to form new vessels. Tumour angiogenesis by releaseof humoral factors (Vacular endothelial growth factor—VEGF) is therebyone of the hallmarks of tumour growth, and also constitutes the targetof novel approaches to treat human neoplasms. Methods to non-invasivelyassess the size, density and integrity of tumour microvessels aretherefore essential to detect malignancies, understand tumour growth,and to target and monitor new therapeutic approaches (Ferrara andAlitalo, 1999).

Dynamic susceptibility contrast imaging, measuring cerebral blood volume(CBV), has for some time been used to characterise cerebralhaemodynamics (Rosen et al., 1990; Rosen et al., 1991a; Rosen et al.,1991b). Together with the specific sensitivity of spin echo (SE) EchoPlanar Imaging (EPI) (Weisskoff et al., 1994; Boxerman et al., 1995) tomicrovessels, this approach provides a unique potential to study theproliferation of capillary sized vessels in tumour angiogenesis. As theability to form new vessels is closely related to the growth potentialand thereby aggressiveness of the tumour, the relation betweenhistological tumour grade and regional CBV has been studied extensively.Aronen et al. studied 19 cerebral glioma patients, demonstrating thatCBV correlated with tumour grade as determined by biopsy or surgery(Aronen et al., 1994). Also, a positive correlation was found betweenCBV and microscopic vascularity as well as mitotic activity.

While the increase in microvascular blood volume reflects vesselformation indirectly, characterising the complex tortuous microvascularstructure in newly formed tumour vessels may be important in quantifyingthe angiogenic process. More importantly, characterising thehaemodynamics of the tumour microvasculature may be essential inunderstanding the retention of drugs in these tumours, and therebyoptimising drug targeting.

The aim of this study was to examine the feasibility of demonstratingabnormal haemodynamics in cerebral tumours showing angiogenic activity,defined as increased microvascular CBV as determined by SE dynamicsusceptibility contrast imaging)

Materials and Methods

Data were acquired as part of a study designed to examine the effects ofdexamethasone (Østergaard et al., 1999b) in brain tumour patients. Thesubjects were consecutive patients seen in the Massachusetts GeneralHospital neuro-oncology clinic with brain tumours or brain tumourrecurrence.

Dynamic Imaging for CBV and CBF Measurements.

Images were obtained using a GE Signa 1.5 Tesla imager retrofitted forEPI capabilities (Instascan, Advanced NMR Systems, Wilmington, Mass.).All subjects received 0.2 mmol/kg of a Gd-based contrast agent (Gd-DTPA,Magnevist, Berlex) delivered by a prototype MR-compatible power-injector(Medrad Inc., Pittsburg, Pa.) at a rate of 5 ml/sec in an antecubitalvein. EPI was performed using TR=1.5 sec, TE=75 msec. Images wereacquired in a 256 by 128 imaging matrix with a 40 by 20 cm field ofview, resulting in 1.6 by 1.6 mm pixels with a slice thickness of 6 mmand an inter-slice gap of 1 mm. Ten slices were obtained simultaneouslyto cover the whole tumour region.

Haemodynamic Variables

Cerebral blood flow (CBF), CBV and flow heterogeneity was determined ona pixel by pixel basis as previously described (Østergaard et al.,1999a; Østergaard et al., 2000). In each image pixel, the distributionof flows (relative flow probability density function) was compared tothat of normal brain by a Kolmogorov Smirnov test to identify areas ofabnormal flow distributions (Østergaard et al., 2000)

Results

FIG. 30 shows structural T₂-weighted image (left) of a female with agrade II astrocytoma, showing edema in the medial part of the leftparietal lobe. The image of relative CBV (middle) shows areas of highCBV (arrow) in the centre of the tumour process, indicating angiogenicactivity. The image at the right shows areas of abnormal distribution offlows compared with normal brain tissue (Østergaard et al., 1999a) ascoloured areas overlayed onto the CBV map. Notice that within the tumourprocess, areas showing highly heterogeneous flow distributions arefound, likely due to the increased tortuosity of the newly formedvessels.

Discussion

Our results indicate that in areas of increased microvascular density,areas of altered flow heterogeneity can be detected, possibly due tochanges in the tortuosity of the microvasculature. This may provide amean for further characterising the angiogenesis in tumours. Thetortuosity of microvessels may be important in the pharmaceuticalmanipulation of the tumours: For optimal local drug effect, ‘trapping’of molecules toxic to the tumour vessels in the tortuous vasculature mayimprove drug action by increasing the time drugs are in contact with thevascular endothelium (Endrich et al 1998). The microscopic haemodynamicinformation brought by flow heterogeneity measurements may therefore beimportant in understanding angiogenesis and optimising drug action inindividual patients.

The current measurements were performed with Gd-chelates and onlyprovide flow heterogeneity measurements in tissue where the contrastagent remains intravascular. Therefore, vascular haemodynamic changeswere not detected in high grade tumours with leaky blood brain barrier,as signal changes due to the T₁ effects of extravascular contrast agentoverwhelms the T₂ change due to intravascular contrast agent. With thedevelopment of blood pool agents, remaining intravascular in many tissuetypes, this technique may also be applicable to extraaxial tumours.

FIG. 30 shows structural T₂-weighted image (left) of a female with agrade II astrocytoma, showing edema in the medial part of the leftparietal lobe. The image of relative CBV (middle) shows areas of highCBV (arrow) in the centre of the tumour process, indicating angiogenicactivity. The image at the right shows areas of abnormal distribution offlows compared with normal brain tissue (Østergaard et al., 1999a) ascoloured areas overlayed onto the CBV map Notice that within the tumourprocess, areas showing highly heterogeneous flow distributions arefound, likely due to the increased tortuosity of the newly formedvessels.

1. Method for determining haemodynamic indices of an organ or of a partof tissue of a mammal including a) determining a time series oftomographic data pertaining to the organ or part of tissue during andafter a bolus injection of a tracer dose to said mammal, the tracerbeing substantially intravascular in said tissue, b) determining a timeseries of concentration data being indicative of the concentration ofthe tracer in arteries of the organ or tissue from the time series oftomographic data, c) determining a residue function of the organ or ofthe part of tissue by deconvolution of the time series of tomographicdata with the time series of concentration data, d) determining adistribution of transit times from the negative slope of the residuefunction, and e) determining a probability density function (PDF) of ahaemodynamic index from the distribution of transit times.
 2. Methodaccording to claim 1, wherein a probability density function (PDF) of anormalised haemodynamic index is determined from the distribution oftransit times, the index being normalised by the value of the integralof said index.
 3. Method according to claim 1, wherein at least one ofthe haemodynamic indices is a quantitative haemodynamic parameterobtained from the PDF.
 4. Method according to claim 3, wherein at leastone of the at least one parameter is obtain from comparison of thedetermined PDF and a previously determined reference PDF.
 5. Methodaccording to claim 4, wherein the parameter is obtained by use of theKolmogorov Smirnov test.
 6. Method according to claim 3 and comprisingthe steps of determining the impulse response function of the organ orof the part of tissue by deconvolution of the time series of tomographicdata with the time series of concentration data, determining therelative tissue flow from the impulse response function of the organ orof the part of tissue, normalising said time series of concentrationdata with the integral of said time series of concentration data withrespect to time, determining the normalised relative tissue flow,respectively the normalised blood volume, of the organ or part of tissueby use of the relative tissue flow and the time series of normalisedconcentration data, and converting said normalised relative tissue flow,respectively normalised blood volume, to an absolute value for thetissue flow (F_(t)), respectively the blood volume, by means of apreviously determined conversion factor, the quantitative haemodynamicparameter being of metabolic significance and determined from the PDFand the absolute tissue flow (F_(t)), respectively the absolute bloodvolume.
 7. Method according to claim 6, wherein a parameter (E)significant for the local extraction of a substance is determined, themethod further comprising the following steps: calculating the relativeflow heterogeneity (w(f)) as a function of the relative flow (f) fromthe distribution of transit times, estimating a value (P) for the localcapillary permeability, estimating a value (S) for the local capillarysurface area, calculating said parameter (E) as the integral value ofthe relative flow heterogeneity (w(f)) multiplied by one minus thenatural exponential function of the negative ratio between i) theproduct of the local capillary permeability (P) and the local capillarysurface area (S), and ii) the product of the relative flow (f) and theabsolute tissue flow (F_(t)) with respect to the relative flow (f). 8.Method according to claim 6, wherein the normalised relative tissueflow, respectively the blood volume, is also normalised with theinjected tracer dose being the ratio between tracer amount and bodyweight of the individual mammal.
 9. Method according to claim 6, whereinthe previously determined conversion factor is in general applicable forthe present method to members of a mammalian specie.
 10. Methodaccording to claim 6, wherein the previously determined conversionfactor is in general applicable for the present method to an organ ortissue of the mammalian specie.
 11. Method according to claim 6, whereinthe previously determined conversion factor is a constant factorapplicable for the present method for any organ or any part of tissue ofthe mammalian specie.
 12. Method according to claim 6, wherein thepreviously determined conversion factor is a constant factor applicablefor all of cerebral tissue of the mammalian specie.
 13. Method accordingto claim 3, wherein the tomographic data comprise information pertainingto subregions of sections of the organ or part of tissue and thehaemodynamic indices are determined for at least a substantial part ofsaid subregions, and wherein quantitative haemodynamic parameters arerepresented as images subdivided into a plurality of pixels eachrepresenting a quantitative haemodynamic parameter pertaining to one ofsaid subregions.
 14. Method according to claim 1, wherein thetomographic data are obtained by means of magnetic resonance imaging.15. Method according to claim 1, wherein the tissue is cerebral tissue.16. Method according to claim 15, wherein the tomographic data areobtained by means of susceptibility contrast magnetic resonance imaging.17. Method according to claim 1, wherein the tissue is renal tissue. 18.Method according to claim 17, wherein the tissue is renal parenchymatissue.
 19. Method according to claim 1, wherein the tissue includestumour tissue.
 20. Method according to claim 1, wherein the tracer is aGd-chelate, such as Gd-DTPA.
 21. Method according to claim 1, whereinthe tracer is an ultra small iron oxide particle (USPIO) intravascularcontrast agent.
 22. Method according to claim 1, wherein the tomographicdata comprise information pertaining to subregions of sections of theorgan or part of tissue and the haemodynamic indices are determined forat least a substantial part of said subregions.
 23. Method according toclaim 1, further comprising using a system for processing of the timeseries of tomographic data pertaining to the organ or the part oftissue, said system residing on a computer having means for producing anoutput representative of at least some of the determined haemodynamicindices.
 24. Method for evaluating the efficacy of a drug or a substanceon an organ or on a part of tissue of a mammal by means of haemodynamicindices of said organ or of said part of tissue obtained by a methodaccording to claim
 1. 25. Method according to claim 24, furthercomprising using a system for processing of the time series oftomographic data pertaining to the organ or the part of a tissue, saidsystem residing on a computer having means for producing an outputrepresentative of at least some of the determined haemodynamic indices.26. Use of information obtained by use of the method according to claim24 for preparing a reference table for use in discrimination of atreatment schedule for an individual mammal or group of mammals forwhich information have been obtained in a manner similar to saidinformation.
 27. Method for obtaining information of the likelihood ofrecovery of an organ or part of tissue in a living mammal upon or duringa period of insufficient vascular supply of said organ or of said partof tissue in the mammal comprising determining haemodynamic indicesaccording to claim
 1. 28. Method for obtaining information of thelikelihood of progression of a chronic or neoplastic disease process ofan organ or part of tissue in a living mammal affecting said organ orsaid part of tissue in the mammal comprising determining haemodynamicindices according to claim
 1. 29. Method for obtaining informationrelevant for discrimination between relevant therapy of an organ or partof tissue in a living mammal upon or a period of insufficient vascularsupply of said organ or of said part of tissue in the mammal comprisingdetermining haemodynamic indices according to claim
 1. 30. Method forobtaining information relevant for discriminating between relevanttherapy of an organ or part of tissue in a living mammal upon thediscovery of a chronic or neoplastic disease of said organ or of saidpart of tissue in the mammal comprising determining haemodynamic indicesaccording to claim
 1. 31. Use of information obtained by use of themethod according to claim 1 for preparing a reference table for use indiscrimination of a treatment schedule for an individual mammal or groupof mammals for which information have been obtained in a manner similarto said information.